EDUC 566 Jan13 1 University of Southern California Rossier School of Education Course Syllabus EDUC 566 - Teaching Mathematics and Science January 2013 Complete the following information when you meet your instructor: INSTRUCTOR: Office Hours: Phone Number: Email: INTRODUCTION AND PURPOSE From a cultural-historical perspective mathematics and science were not considered separate disciplines and those who investigated the natural world were called natural philosophers. Perhaps the acronym STEM - Science, Technology, Engineering and Mathematics – is an attempt to re-integrate these disciplines into a more holistic approach to the teaching and learning about our natural world. The philosophical underpinnings of this course are rooted in the cultural-historical viewpoint and brought to life by challenging students to solve real-world problems through constructive activity and modeling processes. Model-based reasoning and inquiry are the heart and soul of what scientists, engineers, and mathematicians do and therefore a natural means of integrating the STEM disciplines. For instance, we challenge teacher candidates to create a model of a vehicle collision for a movie stunt company. Using a ‘toy’ kit made by the K’nex Education Company student teams construct vehicles and drawings of the vehicles, conduct performance investigations, create tables and graphs of their performance characteristics, form diagrams of the collision, and present their complex model to their colleagues. Such a process emulates the actual practices of the STEM community. We firmly believe that unless our teacher candidates themselves experience this process first hand it is unlikely that they will engage their own students in these critical dimensions of STEM practices. COURSE OBJECTIVES Candidates will develop: an understanding of and flexible application of learning theories to the learning of elementary mathematics and science. general instructional strategies and those specific to mathematics and science. learning experiences in which mathematics and science is related to and integrated with students’ interests, community concerns, and societal issues. balanced assessment practices. a systematic approach based on learning theory to the analysis and design of curricula. an attitude of inquiry toward one’s practice (lessons as experiments) through individual and collaborative study, discussion, assessment, analysis, and classroom –based research and practice. self-efficacy, craftsmanship, collegiality, and flexibility in addressing problems of practice in the classroom, school, and community.
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EDUC 566 Jan13 1
University of Southern California
Rossier School of Education
Course Syllabus
EDUC 566 - Teaching Mathematics and Science
January 2013
Complete the following information when you meet your instructor:
INSTRUCTOR:
Office Hours:
Phone Number:
Email:
INTRODUCTION AND PURPOSE
From a cultural-historical perspective mathematics and science were not considered separate
disciplines and those who investigated the natural world were called natural philosophers. Perhaps the
acronym STEM - Science, Technology, Engineering and Mathematics – is an attempt to re-integrate
these disciplines into a more holistic approach to the teaching and learning about our natural world.
The philosophical underpinnings of this course are rooted in the cultural-historical viewpoint and
brought to life by challenging students to solve real-world problems through constructive activity and
modeling processes.
Model-based reasoning and inquiry are the heart and soul of what scientists, engineers, and
mathematicians do and therefore a natural means of integrating the STEM disciplines. For instance, we
challenge teacher candidates to create a model of a vehicle collision for a movie stunt company. Using
a ‘toy’ kit made by the K’nex Education Company student teams construct vehicles and drawings of
the vehicles, conduct performance investigations, create tables and graphs of their performance
characteristics, form diagrams of the collision, and present their complex model to their colleagues.
Such a process emulates the actual practices of the STEM community. We firmly believe that unless
our teacher candidates themselves experience this process first hand it is unlikely that they will engage
their own students in these critical dimensions of STEM practices.
COURSE OBJECTIVES
Candidates will develop:
an understanding of and flexible application of learning theories to the learning of elementary
mathematics and science.
general instructional strategies and those specific to mathematics and science.
learning experiences in which mathematics and science is related to and integrated with
students’ interests, community concerns, and societal issues.
balanced assessment practices.
a systematic approach based on learning theory to the analysis and design of curricula.
an attitude of inquiry toward one’s practice (lessons as experiments) through individual and
collaborative study, discussion, assessment, analysis, and classroom –based research and
practice.
self-efficacy, craftsmanship, collegiality, and flexibility in addressing problems of practice in
the classroom, school, and community.
EDUC 566 Jan13 2
SUMMATIVE COURSE ASSESSMENT
The Content Area Task – Science. In this assessment you will provide an overview of
important features of your classroom context that influence your instructional decisions. Your response
will provide evidence of: 1) your knowledge of students; and 2) your ability to identify and summarize
important factors related to students’ science learning and the school environment.
Use the learning cycle lesson plan format provided (see Appendix B and week 10 of the
syllabus for details). The plan should include the following information: student academic content
Activity “Pause and Reflect” p. 234. Identify the cognitive function you used.
Class Time. 2 points to be awarded during Class Time for Van de Walle text assignment.
Unit 6 – Week 6
Algebraic Thinking
LEARNING OBJECTIVES
Analyze classroom interactions based on MLE.
Examine in detail how algebraic thinking can be developed starting in elementary school
through mathematics and science.
Identify the components of algebraic thinking and how they can be applied to the learning of
mathematics and science.
Identify, understand, and apply components of model-based reasoning and inquiry.
READER – TEXTBOOK ASSIGNMENTS
1. Textbook Assignments – 6 points. Upload 24 hours before Class Time. A one-point deduction
will be incurred if the responses are late.
Read Van de Walle chapter 14 and respond to the prompts below for the chapters BEFORE
week 6.
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late. Responses must be
written using Word software so that the responses can be copied and pasted to Note Pods that
will be used during Class Time. Your responses will be used during Class Time in break out
groups and whole class discussions. Your instructor may require you to attach all or part of
your paper to the Notes Pod during group or whole-class instruction.
Ch 14 Algebraic Thinking: Generalizations, Patterns, and Functions pp. 254-286
HW Activity 14.3, p 258: What Do You Know about the Shapes? 2 points.
Create another problem and identify the cognitive functions you used to solve the problem you
created.
Ch 14 Activity 14.9 Conjecture Creation. Challenge your students to make up conjectures on
their own after you have modeled the process. Describe in writing the model(s) you created and
how the students responded. 4 points.
2. IMAP CD Assignment – 2 points to be awarded during Class Time.
Watch video clip 13 – Procedural vs. Conceptual Teaching.
EDUC 566 Jan13 23
Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers
to the questions.
View the interactions on video clip 13 and respond in writing to the prompts labeled
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment will be discussed in class. Your responses will be used during
Class Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your responses to the Notes Pod during group or whole-class discussions.
3. Collides – 2 points to be awarded during Class Time. Upload 24 hours before Class Time. A one-
point deduction will be incurred if the responses are late.
Use knowledge from your K’nex experiences to create a model of a two vehicle collision.
See appendix C for details. Include algebraic expressions in your model.
4. Class Time – 4 points to be awarded for the IMAP video responses and Collides model.
5. Annenberg Video – Workshop 2. Biology: Why Are Some Ideas So Difficult? (90 min.) Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air.
See appendix E for the required responses to the video. Be prepared to discuss your written
responses with your forum group. 5 points.
Unit 7 – Week 7
Analyzing Student Thinking
LEARNNG OBJECTIVES
Understand student thinking by analyzing students’ written responses to cognitively demanding
tasks.
Understand and apply proportional reasoning.
Identify, understand, and apply components of model-based reasoning and inquiry.
READER – TEXTBOOK ASSIGNMENTS
1. Learning Cycle Lesson Plan. 4 points. Upload before class time.
Based on comments and suggestions from the first draft submitted in week 5, modify and
improve your lesson.
2. Textbook Assignments – 4 points awarded during class time. Upload the responses 24 hours
before Class Time to the appropriate on-line page before Class Time. A one-point deduction will
be incurred if the responses are late
Read Van de Walle Chapter 18 and respond to the prompts below for the chapters BEFORE
week 7. 2 points awarded during class time.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. Your responses will be used during Class
Randomly estimate and write 10 addition or subtraction fraction problems each on 10 index
cards on 1 side. Quickly look at each card for no more than 5 seconds and write on the back
if it is more or less than 1. Upon completion, explain why you made your decisions.
Upload the responses 24 hours before Class Time to the appropriate on-line page before
Class Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and
pasted to Note Pods that will be used during Class Time.
Your responses will be used during Class Time in break out groups and whole class
discussions.
Your instructor may require you to attach all or part of your paper to the Notes Pod during
group or whole-class instruction.
2. IMAP CD Assignment – 2 points to be awarded during Class Time.
Watch video clip 17 – Sharing of story-problem solutions.
Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers
to the questions.
View the interactions on video clip 17 and respond in writing to the prompts labeled
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment will be discussed in class. Your responses will be used during
Class Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your responses to the Notes Pod during group or whole-class discussions.
3. Class Time – 4 points to be awarded for IMAP CD responses, Van de Walle text assignment.
UNIT 10 – Week 10
Context for Learning and Science Content Task
LEARNING OBJECTIVES
Create a learning event that includes the PACT requirements described below. 10 pts.
1. Annenberg video – Following Children’s Ideas in Mathematics. View the Following Children’s
Ideas in Mathematics video and respond in writing to the prompt: describe what you learned about
the long-term development of students’ mathematical thinking. Be prepared to discuss your written
responses with your forum group. 5 points.
2. Conduct the Tug-of-War Competition described below. 2 points to be awarded during Class
Time. Upload the responses 24 hours before Class Time to the appropriate on-line page before
Class Time. A one-point deduction will be incurred if the responses are late.
Your task is to design a vehicle that will win a tug-o-war against any other vehicle. Each
participant will build a vehicle that they think will beat the competition. Each pair of competitors
will take a picture of their vehicle and send it to their competitor. The competitor will then build
this vehicle from the picture. Verbal or written instructions should be included with the pictures so
each competitor can build the vehicle as intended. Each participant will then conduct the tug-o-war
EDUC 566 Jan13 27
with their own vehicle and the vehicle they built based on their competitors picture and other
information
3. PACT: Context for Learning and Science Content Area Task. 10 points. Upload 24 hours
before Class Time. A one-point deduction will be incurred if the responses are late.
EDUC 566 Jan13 28
Context for Learning
Purpose
The Context for Learning evidence provides a brief overview of important features of your classroom
context that influence your instructional decisions. Your response will provide evidence of: 1) your
knowledge of students; and 2) your ability to identify and summarize important factors related to
students’ science learning and the school environment. You’ll be referring to your description of
students and the teaching context in your responses to the Content Area Task in Elementary
Science.
Overview
If you teach science to more than one class of students, focus on only one class.
Identify learning objectives for both the curriculum content and the development of academic
language related to that content.
Provide descriptive information about the instructional context and instructional resources.
Describe important features of the class that will affect your instructional decisions.
What Do I Need to Do?
Complete the Context for Learning Form. The form is located after the prompts for the
Context Commentary.
Respond to each of the prompts in the Context Commentary.
Context Commentary
Write a commentary of 3-5 single-spaced pages (including prompts) that addresses the following
prompts. You can address each prompt separately, through a holistic essay, or a combination of both,
as long as all prompts are addressed.
1. Briefly describe the following about the context in which the learning segment would be
taught:
a. Type of school/program, (e.g., elementary/middle school, themed magnet, or charter
school)
b. Kind of class (e.g., third grade self-contained, sixth grade core math/science) and
organization of subject in school (e.g., departmentalized, interdisciplinary teams)
c. Degree of ability grouping or tracking, if any
2. Describe your class with respect to the features listed below. Focus on key factors that
influence your planning and teaching of this learning segment. Be sure to describe what your
students can do as well as what they are still learning to do.
a. Academic development
Consider students’ prior knowledge, key skills, developmental levels, and other special
educational needs. (TPE 8)
b. Language development
Consider aspects of language proficiency in relation to the oral and written English required
to participate in classroom learning and assessment tasks. Describe the range in vocabulary
EDUC 566 Jan13 29
and levels of complexity of language use within your entire class. When describing the
proficiency of your English learners, describe what your English learners can and cannot
yet do in relation to the language demands of tasks in the learning segment. (TPEs 7, 8)
c. Social development
Consider factors such as the students’ ability and experience in expressing themselves in
constructive ways, negotiating and solving problems, and getting along with others. (TPE 8)
d. Family and community contexts
Consider key factors such as cultural context, knowledge acquired outside of school, socio-
economic background, access to technology, and home/community resources.
3. Describe any district, school, or cooperating teacher requirements or expectations that might
impact your planning or delivery of instruction, such as required curricula, pacing, use of
specific instructional strategies, or standardized tests.
EDUC 566 Jan13 30
Context for Learning Form
Provide the requested context information for the class selected for this task. This form is designed to be completed electronically. The blank space does not represent the space needed. Use as much
space as you need.
About the subject area/course
1. How much time is devoted each day to specific instruction in science in the class which is the focus
of this task? ______________________________________________
About the students in the class
2. How many students are in the class you are documenting? _____
3. How many students in the class are: English learners ____
Redesignated English Learners _____ Proficient English speakers ____?
4. Please complete the following table about your
English Learners’ latest CELDT scores (if available):
# of Students at Each CELDT Level in Different Modalities
1. Given the description of students that you provided in Task 1.Context for Learning, how do your
choices of instructional strategies, materials, technology, and the sequence of learning tasks reflect
students’ backgrounds, developmental levels, interests, and needs? Be specific about how your
knowledge of these students informed the lesson plans, such as the choice of text or materials used
in lessons, how groups were formed or structured, using student learning or experiences (in or out
of school) as a resource, or structuring new or deeper learning to take advantage of specific student
strengths. (TPEs 4,6,7,8,9)
EDUC 566 Jan13 32
PLANNING MAKING CONTENT ACCESSIBLE
ES2: How do the plans make the curriculum accessible to the students in the
class? (TPEs 1,4,5,6,7,8,9)
Level 1 Level 2 Level 3 Level 4
Plans refer to students’
experiential
backgrounds1, interests,
or prior learning2 that
have little or no
relationship to the
learning segment’s
standards/objectives. OR
There are significant
content inaccuracies in
plans that will lead to
student
misunderstandings.
Plans draw on students’
experiential
backgrounds, interests,
or prior learning to help
students reach the
learning segment’s
standards/objectives.
Plans for the
implementation of
learning tasks include
support3 to help
students who often
struggle with the
content.
Plans draw on students’
prior learning as well as
experiential backgrounds
or interests to help
students reach the
learning segment’s
standards/objectives.
Plans for learning tasks
include scaffolding or
other structured forms
of support4 to provide
access to grade-level standards/objectives.
All components of
Level 3 plus:
Plans include well-
integrated instructional
strategies that are
tailored to address
a variety of
specific student
learning needs.
1 Cultural, linguistic, social, economic
2 In or out of school
3 Such as strategic groupings of students; circulating to monitor student understanding during independent or group work;
checking on particular students. 4 Such as multiple ways of representing content; concrete models; modeling strategies of scientific inquiry; providing
Meaning Importance of subject matter conveyed including the
processes of learning.
Energy and enthusiasm for teaching and learning are
clearly demonstrated.
Transcendence Lessons connected to previous and future learning.
Process questions balanced with fact based
questions.
Teacher models the process of generalizing and asks
students to generalize from specific instances to the
underlying rule
Prompts students’ need to seek and find complex
relationships by providing analogies, models, and
representations.
EDUC 566 Jan13 34
Cycle of Inquiry for Mathematical and Scientific Problem Solving Using Cognitive Functions
Engaging: Approaching and Connecting to Problems
Cognitive Function Teacher definition Evidence
Defining (Understanding)
the problem
Recognizing that something has to be done
and figuring what to do by forming
relationships between the various sources
of information in the problem; devising a
plan; and implementing the plan.
Activating prior knowledge Searching through past experiences in order
to make associations between aspects of the
problem and similar aspects of past
experiences with similar problems.
Analyzing Breaking a problem into its parts and
figuring how the parts are connected or
related to one another; determining which
parts are relevant and which are irrelevant;
and identifying missing parts or
information.
Visualizing Generation of a symbolic, figural, or
pictorial representation of a verbal
stimulus.
Paraphrasing through
rereading
Rewriting, rewording, or restating in your
own words the problem you have just read,
seen, or heard.
Systematic exploration and
planning
Exploring the problem in an organized and
orderly manner, representing the problem
in multiple ways, and constructing a logical
plan to solve the problem.
Comparing Looking for similarities and differences
between two or more objects, events, or
situations in the problem.
EDUC 566 Jan13 35
Exploring: Discovering relationships and patterns; employing tools; explaining possible solution paths, concepts and strategies while
problem solving; manipulating problem elements and representations.
Cognitive Function Teacher definition Evidence
Analogical reasoning Thinking about, representing, and exploring
the problem and ways to solve it based on
analogs, models, and examples from prior
experience.
Modeling Designing a representation of a system with
interactive parts and with representations of
those interactions. Designing models can be
performed with the use of conceptual,
physical, mathematical, and computation
models, or combinations of these.
Forming relationships Making connections between
representations, objects, events, or
situations in the problem.
Forming functional
relationships
Making connections between two or more
things that are changing their values in the
problem in such a way that the changes are
related or are working together in an
interdependent way.
Hypothetical thinking
(Using inductive and
deductive thinking)
If …. Then… thinking. Making a
conjecture (or educated guess) about the
solution to the problem, and searching for
the logical evidence to support the claim or
deny it.
Providing logical evidence -
falsifying
Giving and explaining details, clues, and
proof that connect together and make sense
for supporting a tentative solution to the
problem.
Conserving Constancy Identifying and describing what stays the
same in terms of an attribute, concept or
relationship within the problem while some
other things are changing.
EDUC 566 Jan13 36
Explaining, Elaborating, and Validating: Determining whether a solution is complete and moving beyond a particular problem by
generalizing to other situations
Cognitive Function Teacher definition Evidence
Evaluating Determining the reasonableness of the
solution in the context of the original
problem.
Inductive thinking Taking aspects from various details that
seem to form a pattern, categorizing them
into general relationships of attributes
and/or behaviors, and organizing the results
to form a general rule, principle, formula,
recipe, or guide that can be applied to solve
similar problems.
Deductive thinking Applying the newly found solution, general
rule, principle, or formula to a novel
problem, situation, or a set of details.
EDUC 566 Jan13 37
Appendix B
The Learning Cycle Model of Instruction
The learning cycle is a research-supported, constructivist instructional model based on how humans learn. From a constructivist
perspective, learning can be perceived as a conceptual transformation: “The learning theory that emerges from Piaget’s work can be
summarized by saying that cognitive change and learning a specific direction take place when a scheme, instead of producing the expected
result, leads to a perturbation, and perturbation, in turn, to an accommodation that maintains or reestablishes equilibrium.” (von
Glasserfeld, 1995, p.68). The learning cycle is useful in science and mathematics for organizing curricula at the unit and daily lesson plan
level.
The Five Phases of the Learning Cycle
1. Engagement
In the first phase the teachers develops a ‘hook’ or context to capture the student’s attention. A hook or context provides motivation
that develops anticipation and induces curiosity and suspense. Selected tasks should be cognitively demanding (see criteria for cognitively
demanding tasks). Examples include:
Hands-on
Scenario – real world or teacher created
Demonstrations – discrepant or ill-structured events
Simulations and games
Observe: plants growing; animal behavior; phenomena depicted on video
Use a set of materials to solve a given problem
Minimize or maximize something
Identify an unknown
Field trips
The activities of this phase make connections to past and future activities. The connections depend on the learning task and may be
conceptual or procedural. Successful engagement results in students being puzzled and actively motivated in the learning activity.
Planning for the engagement and exploration phase
What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand
about mathematics/science as a result of this lesson)?
EDUC 566 Jan13 38
In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know
in order to begin to work on the task?
What are all the ways the task can be solved?
Which of these methods do you think your students will use?
What misconceptions might students have?
What errors might students make?
What are your expectations for students as they work on and complete this task?
What resources or tools will students have to use in their work?
How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work
individually or in small groups/pairs? Will students be partnered in a specific way? If so in what way?
How will students record and report their work?
How will you introduce students to the activity so as not to reduce the demands of the task?
What will you hear that lets you know students understand the task?
2. Exploration
Exploration activities are designed so that during class students have common, concrete experiences that begin building concepts,
processes, and skills. In Piagetian terms, engagement brings about disequilibrium while exploration initiates the process of equilibration.
The aim of exploration activities is to establish experiences that a teacher can use later to formally introduce a concept, process, or skill.
As a result of their mental and physical involvement in the exploration activity, students establish relationships, observe and identify
patterns, identify variables, and pose questions. The teacher guides the students as they explore, suggesting strategies to use and monitors
levels of frustration.
Teacher actions during exploration include the function of stimulating students’ mathematical and scientific constructions via the
introduction of new mathematical/scientific ideas into a classroom conversation (Lobato, et al. 2005). These actions may include:
1. Describing a new concept.
2. Summarizing student work in a manner that inserts new information into the conversation.
3. Providing information that students need in order to test their ideas or generate a counterexample.
4. Asking students what they think of a new strategy or idea (perhaps from a “hypothetical” student).
5. Presenting a counterexample that the teacher has not seen any students introduce and thinks no one will.
6. Engaging in Socratic questioning in an effort to introduce a new concept.
7. Presenting a new representation.
EDUC 566 Jan13 39
As students are working independently or in small groups:
What questions will you ask to focus their thinking?
What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?
What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the
representations?
What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?
What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s
ideas?
How will you ensure that students remain engaged in the task?
What will you do if a student does not know how to begin to solve the task?
What will you do if a student finishes the task almost immediately and becomes bored and disruptive?
What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster
of their work)?
3. Explanation
The process of explanation provides the students and teacher with a common use of terms relative to the learning task. The teacher
directs student attention to specific aspects of the engagement and exploration activities. Students are asked to give their explanation of
what occurred (or attempt to answer the guiding question). The teacher introduces a mathematical or scientific explanation in a direct and
formal manner. Explanations are ways of listing, labeling, and ordering the exploratory experiences. The teacher should base the initial part
of this phase on students’ explanations and clearly connect the explanations to experience in the engagement and exploration phases. The
explanation phase can be teacher-, textbook- or technology-directed. Teachers commonly use oral explanations, but there are other
strategies, such as reading, video, film, and educational courseware. This phase continues the process of cognitive construction and
provides scientific and mathematical words for explanations. In the end, students should be able to explain exploratory experiences using
common mathematical /scientific terms.
How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:
Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?
In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas
that are the focus of your lesson?
What specific questions will you ask so that students will:
make sense of the mathematical/scientific ideas that you want them to learn?
expand on, debate, and question the solutions being shared?
make connections between the different strategies that are presented?
look for patterns?
EDUC 566 Jan13 40
begin to form generalizations?
What will you see or hear that lets you know that students in the class understand the mathematical/scientific ideas that you intended for
them to learn?
4. Elaboration
Once students begin developing an explanation of their learning tasks, it is important to involve students in further experiences that
extend or clarify the concepts, processes, or skills. In some cases students may still have misconceptions or they may only understand a
concept or procedure in terms of the exploratory experience. Elaboration activities provide further time and experience that contribute to
learning.
5. Evaluation
Students need feedback on their progress and this can occur informally or formally. Informal assessment (formative) occurs from
the beginning of the teaching sequence whereas formal assessment is best done after the elaboration phase.
As you write the specifics for each phase in the “What the teacher/student does,” estimate the time it will require and place the estimate
under the name of each phase.
Learning Cycle – generalized lesson format
Phase Purpose What the teacher does What the student does
Engage
(time)
To elicit students’
interest in the
concept(s).
1. Creates interest.
2. Generates curiosity.
3. Raises questions.
4. Identifies what the
students know about the
topic.
5. Gives a general
introduction about what the
student will be studying.
1. Asks questions, such as: Why
did this happen? What do I
already know about this? What
can I find out about this? How do
I approach this task?
2. Shows interest in the topic.
Explore
(time)
1. Provides experiences
needed for
understanding.
2. Stimulates inquiry.
3. Provides students
1. Encourages students to
work together without
direct instruction from the
teacher.
2. Observes and listens to
1. Thinks freely, but within the
limits of the activity
2. Uses previously acquired
strategies (or develops new ones),
skills, and concepts to find
EDUC 566 Jan13 41
with the opportunity to
make their own
discoveries and to figure
things out for
themselves.
4. Reveals students’
ideas and thoughts.
5. Sets the stage for
more structured
activities.
students as they interact.
3. Asks probing questions
to redirect students’
investigations when
necessary.
4. Initiates introduction of
mathematical/scientific
concepts when necessary:
Description of a new
concept which can include
an idea, the meaning
associated with a
mathematical symbol, why
something works, an
image, a relationship, or
connections among ideas
or representation;
summarizing student work
in a manner that inserts
new information into the
conversation; provide
information that students
need in order to test their
ideas or generate a
counterexample; ask
students what they think of
a new strategy or idea,
perhaps from a
hypothetical student;
present a counterexample
that the teacher has not
seen any students introduce
and thinks no one will;
engage in Socratic
questioning in an effort to
solutions
3. Forms new predictions and
hypotheses
4. Tests predictions, conjectures,
and hypotheses
5. Tries alternatives and
discusses them with others
6. Records observations and
ideas
7. Suspends judgment
EDUC 566 Jan13 42
introduce a new concept;
present a new
representation.
5. Elicits responses to
initiation of concepts.
6. Proves time for students
to puzzle through
problems.
7. Acts as a
consultant/coach for
students.
Explain
(time)
1. Introduce new
concepts, ideas, skills,
relationships, solutions,
and explanations.
2. Verify or validate
students’ ideas,
discoveries, solutions.
3. Challenge students’
alternative concepts.
1. Encourages students to
explain concepts and
definitions in their own
words
2. Asks for justification
(evidence) and clarification
from students
3. Uses students’ previous
experiences as the basis for
explaining concepts
4. Formally provides
definitions, explanations,
and new labels
1. Explains possible solutions or
answers to others.
2. Listens critically to another
students’ explanations offered by
the teacher.
3. Refers to previous activities.
4. Uses recorded observations in
scientific/mathematical
explanations.
Elaborate
(time)
1. Correct students’
misunderstandings.
2. Broaden and deepen
students’
understandings.
3. Provide the
opportunity for students
to practice the new ideas
1. Expects students to use
formal definitions and
explanations.
2. Encourages students to
apply the concepts and
skills in new situations and
tasks.
3. Reminds students of
1. Applies new labels,
definitions, explanations, and
skills to new, but similar,
situations.
2. Uses previous information to
ask questions, propose answers,
make decisions, create and solve
similar problems, design
EDUC 566 Jan13 43
and skills so they
develop the feeling of
being competent.
4. Promote
generalization and
transfer of learning.
alternative explanations
and probes them.
4. Refers students to data
and evidence and asks:
What do you already
know? Why do you
think…?
experiments.
3. Draws reasonable conclusions
from evidence
4. Records observations and
explanations.
5. Checks for understanding
among peers.
Evaluate
(time)
1. Assess students’
level of conceptual,
procedural and problem
solving understanding.
1. Observes students as
they apply new concepts
and skills
2. Assesses students’
knowledge and/or skills
3. Looks for evidence that
students have changed
their thinking or behaviors
4. Allows students to
assess their own learning
and group-process skills
5. Asks open-ended
questions, such as: Why do
you think…? What
evidence do you have?
What do you know about?
How would you explain?
1. Answers open-ended questions
by using observations, evidence,
and previously accepted
explanations.
2. Demonstrates an
understanding or knowledge of
the concept or skill.
3. Evaluates his or her own
progress and knowledge.
4. Asks related questions that
would encourage future
investigations.
Use the following format for your Learning Cycle lesson in weeks 5, 7, and 10. Respond to all of the bulleted prompts in the column
“What the Teacher does”. Fill in what you expect the student will do cognitively (use the cognitive functions found in appendix D) in the
column “What the student does.”
EDUC 566 Jan13 44
5E Time
Frame
What the
teacher does
What the
student does Prompts
En
ga
ge
As students are working independently or in small groups:
In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin
to work on the task?
What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand about
mathematics/science as a result of this lesson)?
What are all the ways the task can be solved?
Which of these methods do you think your students will use?
What misconceptions might students have?
What errors might students make?
What are your expectations for students as they work on and complete this task?
What resources or tools will students have to use in their work?
How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small
groups/pairs? Will students be partnered in a specific way? If so in what way?
How will students record and report their work?
How will you introduce students to the activity so as not to reduce the demands of the task?
What will you hear that lets you know students understand the task?
Ex
plo
re
As students are working independently or in small groups:
What questions will you ask to focus their thinking?
What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?
What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the representations?
What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?
What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s ideas?
How will you ensure that students remain engaged in the task?
What will you do if a student does not know how to begin to solve the task?
What will you do if a student finishes the task almost immediately and becomes bored and disruptive?
What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster of their work)?
Ex
pla
in
How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:
Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?
In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas that are the focus
of your lesson?
What specific questions will you ask so that students will:
make sense of the mathematical/scientific ideas that you want them to learn? expand on, debate, and question the solutions being shared?
make connections between the different strategies that are presented?
look for patterns? begin to form generalizations?
What will you see or hear that lets you know that students understand the mathematical/scientific ideas that you intended for them to learn?
Ela
bo
rate [No prompts]
Ev
alu
ate [No prompts]
EDUC 566 Jan13 45
Learning Cycle Lesson Scoring Rubric
1 or
1-2
2 or
3-4
3 or
5-6
or
7-8
Learning cycle
lesson All phases of the
LC are not
clearly elaborated
based on
descriptions
provided in the
template.
A significant
prompts in each
phase of the
learning cycle are
clearly addressed.
Only a few
cognitive
functions for
each phase of the
LC are identified.
Most are not
clearly applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
A significant
number of
prompts in each
phase of the
learning cycle are
not clearly
addressed.
Only a few
cognitive
functions for
each phase of the
LC are identified.
Most are not
clearly applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
Most, but not all,
prompts in each
phase of the
learning cycle are
clearly addressed.
Cognitive
functions for
each phase of the
LC are identified
but not clearly
applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
All prompts in
each phase of the
learning cycle are
clearly addressed
based on
descriptions
provided in the
template.
Cognitive
functions for
each phase of the
LC are identified
and applied to
students’ learning
of the
math/science
concepts.
EDUC 566 Jan13 46
Appendix C
K’nex Vehicle Gravity Design Competition
The Scenario
The National Automobile Association is looking for engineering teams to design, construct, and test
gravity powered vehicles that can travel in a straight line for six meters from the end of an 18 inch high
ramp.
Contest procedures and rules
1. Open up your kit and investigate all of the components.
2. Create a ramp for your vehicle that is 12 inches high at one end. The ramp can be as long as
you want but the vehicle release point must be no more than 12 inches above the floor.
3. Design and test your first vehicle. Your first vehicle may not travel the full six meters from the
end of the ramp.
4. Draw a sketch of this first vehicle, no matter how far it traveled.
5. The sketches must use lines and geometric shapes that represent the actual structural pieces that
the vehicle was built from. The sketches should also include the actual number and names for
the pieces.
6. The design sketches must show a top and a side view projection.
7. The sketches must be smaller scaled down versions of the vehicle that will be built.
8. The vehicle must travel 6 meters in a straight line from the end of an 18 inch high launching
ramp.
9. After you design, test, and sketch the first vehicle, you will redesign the vehicle a second and
third time. For the second and third redesign include a new top and side sketch of the modified
vehicle along with the number of each of the different pieces that were used.
Engage
Vehicle Design 1 – make a top view and side view sketch of your first vehicle no matter how far it
traveled down your 12 inch high ramp. The sketches must use lines, circles, and other geometric
shapes that represent the actual structural pieces that the vehicle will be built from.
Top View
EDUC 566 Jan13 47
Side View
EDUC 566 Jan13 48
Explore
Vehicle 1
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you used to build your first vehicle.
After you build your first vehicle, you will release it from the top of the 12 inch high ramp.
Why is it important that you always release your vehicle from the top of the ramp?
What do you think the variables are so far in this investigation?
What are the values of the variables?
2. Let your vehicle roll down from the top of the ramp without pushing it.
3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For
instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went
about one-fourth of the way then it went 25% of the way. Express this distance as a decimal
and a fraction. Record these values in Table 1.
4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this
value in Table 1.
5. Make three trials with your vehicle and record your data in the chart below.
Why should you conduct three trials with your vehicle and not just one trial?
EDUC 566 Jan13 49
When the vehicle stops, describe how you are going to measure the distance the vehicle
traveled. Think about the front and back of the vehicle when you write out your procedure.
Describe how you are going to determine whether or not the vehicle has traveled in a straight
line before you measure the distance. How straight does the line have to be before you measure
the distance?
TABLE 1 Original
Vehicle Design
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent
compared to the
actual value?
Express this
comparison as a
percent.
Are there any new variables in this investigation?
If so, what are they?
What do you think the relationship is between the variables you have identified so far?
Distance Vehicle Travels in Meters
EDUC 566 Jan13 50
Vehicle 2
Vehicle Design 2 – make a top view and side view sketch of your second vehicle.
Top View
Side view
EDUC 566 Jan13 51
Vehicle 2
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you will use to build your second vehicle.
What do you think the variables are so far in this investigation?
2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it
travels from the bottom of the ramp.
3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For
instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went
about one-fourth of the way then it went 25% of the way. Express this distance as a decimal
and a fraction. Record these values in Table 2.
4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this
value in Table 2.
Make three trials with your vehicle and record your data in the chart below.
EDUC 566 Jan13 52
TABLE 2
Vehicle 2
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent and
the actual
value?
1. Did vehicle 2 outperform vehicle 1? Why or why not?
2. Are there any new variables in this investigation? If so, what are they?
3. What do you think the relationship is between the variables you have identified so far?
Distance Vehicle Travels in Meters
entimeters
EDUC 566 Jan13 53
Vehicle 3 Vehicle Design 3 – make a top view and side view sketch of your third vehicle.
Top View
Side view
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you will use to build your third vehicle.
EDUC 566 Jan13 54
What do you think the variables are so far in this investigation?
2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it
travels from the bottom of the ramp.
3. Make three trials with your vehicle and record your data in the chart below.
TABLE 3
Vehicle 3
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent and
the actual
value?
1. Did vehicle 3 outperform vehicle 1 and 2? Why or why not?
Distance Vehicle Travels in Meters
EDUC 566 Jan13 55
2. Are there any new variables in this investigation? If so, what are they?
3. What do you think the relationship is between the variables you have identified so far?
Summary of data
Design Type Trial 1 Trial 2 Trial 3 Average
Original vehicle
Second vehicle
Third vehicle
Explain
Look at the data table and describe any patterns that you notice.
What do you think caused the pattern that you noticed?
Make a sketch of the gravity design system that your team has been investigating. Identify critical parts
of this system. This is a model of the gravity design challenge that you have been working on. Be
prepared to explain your model and your investigation to the rest of the class.
Egg-citing Design
The Scenario
Automobile laws in California require all passengers to wear a seat belt. Many cars now have safety
features called air cushions. What is the purpose of these safety devices?
EDUC 566 Jan13 56
The Challenge
As a member of the automotive engineering team you have been assigned the responsibility of
improving the overall safety of the company’s cars. You and your team believe that the current
restraint system of the vehicles needs to be revised, especially since the testing procedures have been
upgraded and more sensitive raw eggs will be used instead of the standard electronic dummy.
The Constraints
1. Each engineer must submit a detailed diagram of their car.
2. Each engineer must submit a procedure for testing their safety system.
3. During the investigation phase engineers will use imitation eggs.
4. Raw eggs, in plastic bags, will be used for the final test.
The Rules
1. All ramps will be 120 centimeters long and must be maintained at a ramp height of 18 inches.
The lower end of the ramp will be butted against a wall.
2. Detailed sketches must accompany each final report. The terms potential and kinetic energy
must be used in the explanation of how the safety system functions. Kinetic and potential
energy are described in the teachers guide found in the kit.
3. During final testing all eggs must be housed inside a plastic bag.
4. Evaluating and rating of the safety system after the final test run is as follows:
Excellent – The shell is not cracked and the yolk is unbroken.
Fair – The shell cracked but the yolk is unbroken.
Unacceptable – The shell cracked and the yolk is broken.
All engineers must prepare a final report that details the safety features implemented, how the testing
was conducted, and the results of this testing. Reports must also include additional safety
recommendations that might be considered.
“Collides” You are the stunt coordinator for the new movie “Collides”. In the movie one of the scenes requires
three types of cars to participate in a chase and a subsequent collision. The cars should have different
sources of energy and travel at different speeds. The producer has given you the following conditions
for the collision:
EDUC 566 Jan13 57
1. The cars must be built from the K’nex kit - Force, Energy and Motion.
2. Two cars are involved in a chase, going the same direction on the same street.
3. Another car is traveling on a different street from the two cars in the chase.
4. The lead car in the chase will make it through the intersection without a collision.
5. The following car in the chase and the car traveling on the other street will collide.
6. The collision takes place at the intersection of the two streets.
7. The minimum distance of the lead chase car and the collision car from the intersection is 120
meters.
Your task is to provide the producer with a model of the collision.
Components of the models that will evaluated for the winning production company.
1. A scale model to depict your collision.
2. Diagrams, graphs, tables, equations, and written explanations to describe the cars’ movements.
3. A video of the actual collision scene along with a formal presentation of the model.
Standards: Algebra I: 5.0, 6.0, 9.0, 15.0
Vehicle Tug-O-War
Your task is to design a vehicle that will win a tug-o-war against any other vehicle. We will use a
playoff elimination system to determine the winner. Each participant will build a vehicle that they
think will beat the competition. Each pair of competitors will take a picture of their vehicle and send it
to their competitor. The competitor will then build this vehicle from the picture. Verbal or written
instructions should be included with the pictures so each competitor can build the vehicle as intended.
Each participant will then conduct the tug-o-war with their own vehicle and the vehicle they built
based on their competitors picture and other information
EDUC 566 Jan13 58
Appendix D
Cognitive Functions – The Prerequisites of Learning*
Input phase – collecting the information
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Clear and
focused
perception
Focused perception; use all
senses to perceive all data
correctly and clearly. Keep
your focus on one spot.
What do you see?
What is here?
Have you perceived everything?
Where do you have to look?
Blurred and sweeping perception. Not
knowing where to start looking, look at
everything as a whole.
Look very quickly here and there.
2. Searching
systematically
Collect the data step by step in
a systematic way so that
nothing is lost and nothing is
done twice.
We are going to look step by step. One by one. In what
order? Let’s start here, on the left at the top, then from
left to right, then the second row, etc.
Look up a word in a dictionary, a place on a map,
check that all words are correctly spelled.
Counting one by one.
Unplanned, impulsive, and unsystematic
behavior.
Criss-cross perception, here-there-
everywhere without rhyme or reason.
Counting the same things twice.
3. Labeling Enrich vocabulary to describe
objects, events and
experiences precisely.
Describe the objects according to their characteristics
and definition.
What are the characteristics? In what way do they
differ? In shape, distance, color, number, size,
direction?
How can we call a four-sided closed figure with equal
sides, but no equal angles?
Lack of, or impaired receptive verbal tools
that affect discrimination (e.g. objects,
events, relationships, etc. do not have
appropriate labels).
Because of lack of correct names to describe
objects, events and relations, with their main
features, they are not adequately observed;
the child does not see a difference e.g.
between a rectangle and a square, it’s the
same for him.
4. Spatial
reasoning
Use concepts to indicate place,
direction, position and
orientation in relation to each
other or to a frame. Be able to
use spatial concepts.
How are things related to each other? Parallel, at a right
angle, central, in the middle of…?
Where is this? (e.g. top-left; bottom-middle; next to…;
left of…; in front of; etc.
In what direction are they running: towards…; coming
from left to right, east to west, north to south?
Lack of, or impaired, spatial orientation, the
lack of stable systems of reference impairs
the establishment of topological and
Euclidean organization of space.
Problems with left/right discrimination.
Problems with map reading.
Problems with drawing simple objects,
especially their 3-D relationships.
Problems with describing where you are and
EDUC 566 Jan13 59
where you want to go.
5. Temporal
reasoning
Use the correct concepts to
describe time and sequence.
Look for data which give you
indication of the sequence of
things and the ordering in
time.
How do you know what comes first and thereafter?
Lack of, or impaired, temporal concepts.
Problems with planning – starting on time.
6. Conserving
constancy
Be attentive that some
characteristics of an object or
a relationship change while
others remain the same.
What changes and what stays the same?
Which characteristics change?
If a square is rotated, does it remain a square?
If gasoline costs $2.00 per gallon how much will you
pay for 5 gallons?
Lack of, or impaired, conservation of
constancies (size, shape, quantity,
orientation) across variation in the factors.
Using additive thinking when
multiplicative thinking is required.
7. Being precise Being attentive to details
when it is important to do so. Have you noticed the details?
Are these two objects really the same height?
Lack of, or deficient need for, precision and
accuracy in data gathering.
Not noticing the place of the comma in a
number.
Not being precise in measuring lengths,
weights, etc.
8. Using more
than one source
of information at
once.
Take into account more
characteristics at the same
time (height, length, width,
number, shape, etc. Feel the
need to collect information
from different sources.
Have you been complete in gathering the data?
Where can you find information on what to do?
How many ways are we being presented with
information on what to do?
Lack of capacity for considering two or
more sources of information at once, this is
reflected in dealing with data in a piecemeal
fashion rather than as a unit of organized
facts.
Dealing with data in a piecemeal fashion
rather than as an organized unit, e.g. with a
school task – text, drawings, numbers
indicating order, tables, maps, index,
dictionary.
9. Activating
Prior Knowledge
Remembering and retrieving
relevant information from
memory.
Where have you seen or heard of this before?
Does this look or sound familiar? Why?
Lack of or deficient need for retrieving
relevant knowledge from long-term memory
in order to make connections among
characteristics of something currently being
considered or a problem to be solved.
10. Analyzing Identifying a structure,
process, concept, object, etc.
as a whole or unit and the
parts or elements the make up
the whole.
What are the parts of this thing?
How are the parts related to one another and to the
whole?
What are the steps of this process or procedure? Are
they in order? Why is this order important?
Impaired or deficient propensity for
breaking material, structures, or processes
into its parts and determining how the parts
relate to one another and to an overall
structure or purpose.
EDUC 566 Jan13 60
Elaboration phase - processing the gathered information
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Defining the
problem
Recognizing the problem and
being able to define it. What’s the problem here?
What do we have to do?
Is there a problem?
What is it?
Does it fit? Is everything all right? Is it correct?
Inadequacy in the perception of the
existence and definition of an actual
problem.
There is little or no awareness that
something doesn’t fit, or it is not right.
Difficulty in getting started because there is
a lack in knowing what to do.
2. Selecting
relevant
information
In a multitude of information,
select the information which
you need to solve the problem
and neglect/eliminated the
rest.
What information do you need to solve the problem?
What do you not need to solve this problem?
What is a key word in this task?
What is the important information and what is not
important information for solving this problem?
Inability to select relevant vs. non-relevant
cues in defining a problem.
Difficulty in finding key words in a reading
passage, and in forming a summary.
Difficulty in selecting the information
which is needed to solve a word problem.
3. Comparing Developing the need to
compare things, to look a
similarities and differences
with other things and events.
In what way are they same? Different?
Expand the repertoire of criteria to compare.
How should we compare these things, by size, color,
shape, quantity, etc.?
What does ‘greater than/less than’ mean?
What does ‘n times as much’ mean?
Let’s look at the first as, what are the words to the left,
now let’s look at the second as, what are the words on
the right of this as?
Prepositional relations compared – eight divided by
four compared to eight into four.
Lack of spontaneous comparative behavior
or limitation of its application by a restricted
need system.
Compare on the basis of only one arbitrary
criterion.
Compare on the basis of non-relevant
criteria.
Lack of spontaneous comparison with prior
knowledge.
Difficulty in identifying the lack of
correspondence between mathematical
symbols and the words they represent (e.g.
if the expression eight divided by 2 is
translated word-for-word in the order in
which it is written, the resulting
mathematical expression 82 would be
incorrect .
EDUC 566 Jan13 61
4. Broadening
your mental field
Have an overview, take into
account as many factors as
possible. Effective memory
capacity. Analogous to
computer with a large hard
disk and a fast retrieval speed.
We are confronted here with a mass of data. Can’t we
put them into order? Can’t we recognize groups? What
things could belong together? On what basis?
How can we memorize better?
Writing down key words.
Making a schema, a table, a matrix.
Keeping an agenda.
Have a system of visual retrieval (post-it-notes),
writing in the margins.
Narrowness of the mental field.
Forget things easily.
Deal with things as pieces one by one,
rather than in units or chunks.
Not able to process two things at the same
time.
When you learn something new, you forget
the previous learning(s).
5. Forming
relationships,
making
connections
Put things in relation to each
other.
Cause – effect relations.
Means – ends relations.
Have you seen something similar before?
How are these connected?
Is A the cause of B, or does B cause A? Why?
Episodic grasp of reality.
Dealing with events and objects as if there is
no connection between them, in an episodic
way.
6. Need to pursue
logical evidence
Have a need to justify the
answer and be able say why
choose a certain solution.
Spontaneously search for date
to justify a statement.
How do you know this? How do you know whether
your answer is correct?
Why is it correct? Why not?
Explain your answer.
Lack of, or impaired, need for pursuing
logical evidence.
Giving an answer but not knowing why the
answer is right or wrong.
The student accepts statements without
critically examining them.
Beliefs are either unexamined and
unjustified or justified by their
correspondence with the beliefs of an
authority figure, such as a teacher or parent.
7. Internalizing
and representing
information
Composing a mental image of
the information. Visualizing
and mentally representing
information in different ways.
Make a mental picture of the information.
Visualizing the information in more than one way.
Lack of, or impaired interiorization.
8. Hypothetical
deductive –
predictive
thinking
If … then thinking. Represent
mentally what could possibly
happen, if… Inference: draw a
conclusion; one thing follows
from another.
What do you think could happen?
What do you predict will happen?
What could the possible solutions be?
What can you infer from this statement?
What can you conclude from this?
Lack of, or impaired, inferential-
hypothetical thinking.
Limited capacity to come up with
possibilities.
9. Developing
strategies to test
hypotheses
Check a hypothesis mentally:
what could be the effect of an
event. Find means to check
and confirm a hypothesis.
If a possibility is thought of,
look for data which confirms
or refutes it.
Shall we look for a strategy to check it?
Let’s compare with the model, analyze the model’s
characteristics, make a drawing, schema, write down
the steps, look for more data; use additional reliable
sources of information like encyclopedias, use a
calculator after making the operations mentally; use the
reverse operation.
Lack of, or impaired, strategies for
hypothesis testing.
Have a need to check solutions in a concrete
rather than a mental way.
Have no need to check at all.
Difficulty in representing possible effects.
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10. Selecting a
frame of
reference,
structure, or
framework for
problem solving
Choose a framework in which
a solution can be found. Where shall we look for a solution?
What operation should we do here: is this a
multiplication problem or an addition problem? Is this a
problem of classification?
Do we need a science text or dictionary? Shall we got
to the library or ask an expert?
Lack of, or impaired ability to define the
framework necessary for problem solving
behavior.
Have no idea where to start looking.
Have no idea which operation to choose.
11. Planning
systematically
Represent the steps toward a
solution one by one. What are the steps we have to take in order to arrive at
our goal?
What are you going to do first? And then? And then?
Lack of, or impaired, planning behavior.
Start working in an unsystematic way.
12. Categorizing Develop vocabulary for
superordinate words and
concepts to indicate cognitive
categories and describe mental
operations.
Let’s compare – find the similarities and differences.
This belongs to a larger group, let’s find the class or
category that it belongs to. What is the name of this
category?
Let’s order these things. What comes next?
Let’s think this through, what thinking action(s) do we
need to use to solve this problem?
Non-elaboration of certain cognitive
categories because the verbal concepts are
not a part of the individual's verbal
inventory (on a receptive level) or they arc
not mobilized at the expressive level.
Lack of words to describe categories.
13. Accounting
for all
information
Encourage counting. Make an
inventory. How much do you have?
Are you sure we did not miss anything?
Lack of, or impaired summative behavior.
Paraphrasing
Through
Rereading
After reading (or hearing)
something, restating the main
idea in your own words.
Tell me in your own words what I just said.
Tell me in your own words what you just read.
Tell me exactly what the problem is.
Lack of or impaired need for writing or
saying something in your own words that
you have just read or seen (or heard).
Transforming a
Representation
Changing the modality of a
representation from one type
to another.
Make a diagram of what you just read.
Make a picture with stick figures to represent this
problem or story.
Use numbers and symbols to represent the
relationships and things in this word problem.
Make a table, a graph.
Lack of or impaired need for changing the
modality of presentation from one form to
another.
Inductive
Thinking
Forming relationships among
data or information so that a
general rule or formula can be
created.
What is common to all of these?
Do you see a pattern?
How could you classify these things?
Write out the rule or formula that clearly states the
relationship(s) that you discovered.
Lack of or impaired propensity for forming
abstract relationships among items or data
that seem to form a pattern, categorizing
them into general relationships, and
organizing the results to form a general
rule, principle, formula, recipe, or guide.
Analogical
Reasoning
Transferring relationships
discovered in one task to a
new task where the prior
discoveries will be helpful in
What have we just learned that may be helpful in
solving this problem?
Do we have any examples or models that will help us
Lack of or impaired need for transferring
relational information from existing
concepts to a new problem that needs to be
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solving the new task. solve this problem? solved. Deficiency of abstracting a solution
strategy from a previous problem and
relating that information to a new problem
that one is trying to solve.
Synthesizing
Connecting things to form a
new structure. How can we modify these things and then put them
together to make something new?
Lack of or impaired propensity to connect
elements together to form a coherent or
functional whole so that a new pattern or
structure emerges that is not just a
reordering of the elements.
Output phase – expressing the solution correctly
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Expressing
yourself clearly
Put yourself in the other
person’s shoes in order to
communicate your answer
clearly.
I can understand what you mean, but please, could you
say your answer so that others can understand it as
well?
I can see you know, but nobody else sees it.
Encourage a student whose habit is to speak in one
word sentences, to speak in full sentences.
Egocentric communicational modalities.
A student who does not bother to write
down or tell his answer, because he is
satisfied he knows it.
Difficulty in explaining a familiar way to go
somewhere.
2. Projecting
virtual
relationships
Make hidden relations
explicit. Make relationships visually obvious with graphic
organizers, markers, schemata, arrows, etc.
Infer future events from present trends in a sequence of
beliefs on what causes the seasons and their explanations for the phases of the moon.
What is the theme of this workshop? The theme of Workshop One is "Eliciting Student Ideas."
Pre-Workshop Activity
Prior to this workshop, workshop participants should spend 5-10 minutes interviewing a student and an adult about what
causes the changes in the seasons. Record their responses. Did you discover some good ways to uncover students' ideas?
Explain.
Whom do we see in the videotape? We see several Harvard students and faculty who are enormously
confused about what causes the seasons. We also see Heather, an articulate, intelligent high school
student who has a great many ideas about astronomy. Interviews with Heather both before and after
her classroom lessons about astronomy reveal that she has learned much but is still confused about
some key aspects of the subject.
What happens in the videotape? While some of Heather's ideas after instruction are solid, others
seem wildly "off base" from a scientist's point of view. Some of her ideas stubbornly resist change,
either in the classroom or during on-camera challenges.
What problem does this workshop address? Many of us think that the cause of the seasons has
something to do with our distance from the sun, even though this "wrong idea" was never taught to us.
Why is it we seem to learn some things that teachers don't teach us?
What teaching strategy does this workshop offer? Many techniques for eliciting student ideas have
been tested in the classroom. Interviews with students, poster presentations, prediction questions,
group discussions, and journal keeping are some of the most common approaches. This workshop will
address interviewing techniques and journal keeping.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
1. Is understanding the causes of the seasons or lunar phases important in the lives of students?
2. Why is an understanding of basic scientific principles important for all citizens?
3. What are some surprising ways in which a good science understanding can enhance the abilities
of non-scientists to perform their work and live their lives? (For example: Could chemical
understanding affect the work of professional cooks and homemakers; could understanding
weather and fluid dynamics help make better airline pilots and sailors; and could understanding
how plants make food affect anyone who gardens?)
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4. What are some examples of important social or political issues that require a scientific
understanding by voters and policy makers? (For example: Would knowledge of science be
important for understanding toxic waste, screening for genetic diseases, global warming, or
energy conservation issues?)
Week 6 Annenberg Video Assignment
For Week 6 go to the Annenberg Private Universe Project in Science website by entering this URL in
your browser:
http://www.learner.org/resources/series29.html
Click on the icon titled VoD for Workshop 2. Biology: Why Are Some Ideas So Difficult?
Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air. What is the theme of this workshop? The theme of Workshop Two is "discovering the scope of student ideas".
Whom do we see in the video? Jon, a seventh-grade student, is interviewed before and after a traditional lesson on photosynthesis. Bob Holden, Jon's teacher, watches the video of Jon's interviews, discovering that Jon's problems in biology concern his confusion about the physics and chemistry of matter and energy. Jon also has no concept of energy and the relationship of energy to chemical changes. He seems to be missing the concept that chemical changes may either require an input of energy or may release energy.
What happens in the video? Interviews with Jon suggest that teaching can be more effective when the full scope of a student's ideas are considered.
What problem does this workshop address? Photosynthesis is among the most widely taught of all concepts in biology. Why, then, do many people have difficulty grasping the central idea of photosynthesis-that most of the substance of plants comes from the air?
What teaching strategy does this workshop offer? Among many possibilities to help students reflect on their own thinking, we offer such techniques as concept mapping and journal keeping.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
1. Devise a simple explanation, demonstration, or activity for understanding how plants convert carbon dioxide from the air and water from the ground into food through photosynthesis.
2. Invent a way that allows even the skeptical students to convince themselves that the air does, indeed, have mass/weight. Whenever possible, allow students to test the idea.
3. Often the ideas established prior to and outside the teaching of a subject block learning. How can this problem be addressed in the classroom? For instance, the student in the video has trouble
understanding photosynthesis because of his belief that air has no weight. An understanding that air
is made of invisible particles with weight is usually a topic for chemistry or a physics lesson, and a
lack of this understanding prevents the student from learning an idea in biology.
Week 8 Annenberg Video Assignment
For Week 8 go to the Annenberg Private Universe Project in Science website by entering this URL in
your browser:
http://www.learner.org/resources/series29.html
Click on the icon titled VoD for Workshop 5. Vision: Can We Believe Our Own Eyes?
Explores the origins of student ideas to find out whether experience equals learning. Shows how
experience can work for or against learning because students can disbelieve concepts that they have
“learned.”
What is the theme of this workshop? The theme of Workshop Five is "the origins of student ideas."
Whom do we see in the video? Richard and Karen, eighth graders, and Conor, a fifth grader, are three
students who constructed many of their ideas from personal experience, television nature specials, and
classroom activities. Conor blends the various resources and constructs rich and imaginative
explanations of light and vision; Richard vacillates between scientific and non-scientific ideas, even
after instruction; and Karen never waivers from her personal construction about vision.
What happens in the video? Students of various ages discuss their ideas of how we "see." Their
ideas, many of which seem to come from sources outside of school, often differ from those accepted
by scientists. Where do students' ideas come from and can (or should) they be changed?
What problem does this workshop address? Although mirrors are among the most common of
scientific devices, they remain enigmatic. The average adult in the United States may use a mirror
30,000 times in a lifetime. Why is it that, even with all of this experience, so many adults still cannot
answer simple questions about the properties of mirrors?
"Can We Believe Our Own Eyes?" addresses students' "conceptual change," a process by which
students replace old ideas when new ones become more acceptable. This workshop explores how
students construct ideas from the many sources available to them. Television, radio, books, parents,
teachers, and peers all play a role in promoting the ways in which students see and understand natural
phenomena. In contrast, seeing often contradicts their understanding and, as a result, seeing is not
always believing. What can we learn about children's concepts of light and vision that can shed some
light on this problem?
What teaching strategy does this workshop offer? The role of students' experience can be very
powerful in shaping their ideas and beliefs. Does this experience always lead to a better understanding?
Teachers learn to confront students' understanding by offering alternative experiences that contradict
old ideas.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
1. Do you think it is possible for a teacher to control the way a student interprets ideas? Please
explain your response.
2. When teachers see their students espousing non-scientific ideas picked up from television,
books, and other sources, often the immediate reaction is to suggest ways to eradicate the
sources of "misconceptions" and replace the alternative ideas with the science ideas. The more
experience we have with something, the more difficult it can be to understand. Experience can
reinforce or create misconceptions. Experience does not equal understanding. Should or can
we as educators "misconception-proof" the student's world? Explain. 3. Light allows us to see and yet light itself seems invisible. What activities might we
devise to help students in grades K-3 develop concrete images of the abstract concept of
light?
Following Children’s Ideas in Mathematics - Due Week 10
An unprecedented long-term study conducted by Rutgers University followed the development of
mathematical thinking in a randomly selected group of students for 12 years - from 1st grade through
high school - with surprising results. In an overview of the study, we look at some of the conditions
that made their math achievement possible.
Private Universe Project in Mathematics. Following Children’s Ideas in Mathematics.
http://www.learner.org/resources/series120.html
Using the Forum, describe what you learned about the long-term development of students’
mathematical thinking. Respond to the post of at least one other student.