Standards-Based Instruction Secondary Mathematics Teachers Curriculum Day Chattahoochee HS/Taylor Road MS August 4, 2011 Presented by Pamela A. Seda, Ph.D.

Standards-Based Instruction

Secondary Mathematics Teachers Curriculum DayChattahoochee HS/Taylor Road MS

August 4, 2011

Presented by Pamela A. Seda, Ph.D.Director of Secondary Mathematics

Give One, Take OneScenario: Let’s say you have been invited to visit every math classroom in a school that has just received the award “Best Mathematics Instruction in the Country.” List 4 things that you would expect to see in every math classroom.

Fulton County Schools Effective Standards-Based Classroom Instruction

Definition of Standards-Based Instruction

Using a variety of resources to assess, plan and instruct in a way that encourages students to know what they are learning, why it is relevant, the ways to get there, when they have learned it, and how they can go even further.

LearningThink of something not job related that you have learned to do very well? Skating, horseback riding, painting, etc. Now think about what it took to get you to that level of expertise. What are some things that these experiences have in common?

Three Guiding Principles of Standards-Based Instruction

All students learn more when …• they have a clear vision of the learning target.• they meaningfully interact with the content in a

supportive environment.• given multiple opportunities to learn in a variety of

ways.

Clear Vision of the Learning Target

“Students can hit any target that they can see and that holds still for them.” Stiggins, et. al, 2004 p. 57

Clear Vision of the Learning Target

Clear Vision of the Learning TargetThe Standards are our learning targets, but how clear are they?

• 8th Grade Math Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. i. Simplify expressions containing integer exponents.

Clear Vision of the Learning Target8th Grade Math Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. i. Simplify expressions containing integer exponents.

• Essential Question: How do I simplify and evaluate algebraic expressions involving integer exponents and square roots?

Clear Vision of the Learning Target8th Grade Math Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. i. Simplify expressions containing integer exponents.

• Sample CRCT Problem: Substitute the* with the integer that makes the following statement true. p*p2 = p8

A. 4B. -10C. 6D. 8

Clear Vision of the Learning Target8th Grade Math Standard: M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. i. Simplify expressions containing integer exponents.

• Open-ended Assessment Problem: For the expression below, find values for a, b, c, d, e, and f so that the expression simplifies to 3x2y-3. Show all work, including an explanation of why you chose the selected values.

fe

cb

ydxyax

Clear Vision of the Learning TargetFor the expression below, find values for a, b, c, d, e, and f so that the expression simplifies to 3x2y-3. Show all work including an explanation of why you chose the

selected values.

fe

cb

ydxyax

Clear Vision of the Learning TargetSample Student Work with Commentary

•Student work demonstrates understanding of the quotient rule for exponents.•Work is neatly shown •All calculations are not accurate (0 - -3 ≠ -3)•Answer not written in a complete sentence. •Checking of solution is shown.•Explanation should have provided more details about thought processes.

Clear Vision of the Learning TargetIf teachers don’t have a clear vision of the learning target themselves, …

• How can they determine how close their students are to learning the target?

• How can they provide their students the guidance they need for reaching that target?

• Medals and Missions video clip

Clear Vision of the Learning Target• The best way to get a clear vision of the learning

target is to work high quality assessment items yourself, and try to think like your students.

• Ask yourself, “What are some difficulties, misconceptions, mistakes, and/or errors might my students encounter while working these types of problems?”

Meaningful Interaction with the Content• Mathematically Meaningful for Students – Maintains the

proper balance between concepts, skills, and problem solving“… the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided.” National Mathematics Advisory Panel Final Report, 2008, page xix.

• Personally Meaningful for Students – Answers the question, “Why should my students care about learning this?”

Meaningful Interaction with the ContentConcrete→Pictorial→Abstract (c.p.a)

1. Introduce content conceptually or contextually first2. Then approach the content using drawings and/or

pictures3. Then introduce algebraic and/or symbolic notation

Meaningful Interaction with the ContentTeaching Problem Solving with Heuristics

Heuristic methods are used to speed up the process of finding a satisfactory solution to a problem, where an exhaustive search is impractical (Wikipedia)

• Flexibility• Reversibility• Generalizability

Meaningful Interaction with the ContentFlexibility – diversity in approach to problem solving

• Does anyone have the same answer but a different way to explain it?

• Can you solve it a different way?• Can you draw a different picture?• What is alike/different about your method of

solutions?• Can you use a different model?

Meaningful Interaction with the ContentReversibility – switching from a direct to a reverse train of thought

• Can you think of a counter-example?• Can you give me another problem with the same

answer? Another?• You just gave me the right answer to a different

question! What is a question for that answer?• How would you change the problem so your answer

was larger? Smaller?

Meaningful Interaction with the ContentGeneralizibility – applying a rule already known to produce another rule

• Is that true for all cases?• Do you see a pattern?• Can you predict the next one?• How does this relate to...?• What did you already know that helped you solve

this problem?• Have you ever solved a problem like this before?

Meaningful Interaction with the ContentTraditional problem:

More rigorous problem: If you add me to three-fourths, you end up with seven-eighths. • What fraction am I? • Explain your solution with words, a drawing, and/or a number

sentence.

Which heuristic method(s) apply here? Flexibility, reversibility, or generalizability

Meaningful Interaction with the Content

How many squares do you see?

BINGO PROBLEM

Meaningful Interaction with the Content

How many squares do you see now?

BINGO PROBLEM

How many squares would you see on a 3 x 3 Bingo card?How many squares would you see on an 9 x 9 Bingo card?

Which heuristic method(s) apply here? Flexibility, reversibility, or generalizability

Meaningful Interaction with the Content

Try developing an sample problem for each:

•Flexibility – more than one approach•Reversibility – reversing train of thought•Generalizability – developing a general rule from a pattern

Meaningful Interaction with the ContentWhy should my students care about learning this?

• Relevant – How does it connect to your students’ interests and/or goals?

• Examples: Activities that include family, friends, sports, entertainment,

technology, etc. Use peer pressure to your advantage.

• Non-examples: It’s on the CRCT You’ll get a failing grade if you don’t learn this You’ll need this someday in the future

Meaningful Interaction with the Content“Authentic tasks create a bridge between what is learned in the

classroom and why this knowledge is important to the world outside of the classroom.” Creative Educator website

• Example: Area and Perimeter - Cut out five photographs of various sizes from a newspaper at home, measure the length and width of each photograph to the nearest tenth of a centimeter. Find the area and perimeter of each photograph. With your other team members, arrange your pictures in order from smallest to largest area. Do it again for perimeter. Was the arrangement different? Why or why not?

• Non-example: Traditional textbook problems and worksheets

Meaningful Interaction with the Content

Who is in charge of the learning?• Rick Stiggins Video Clip

Supportive Environment• A supportive environment is a positive

environment where all students are respected and held to high expectations within a community that takes collective responsibility for both behavior and learning.

Supportive Environment• Effective teaching conveys a belief that each student can and is

expected to understand mathematics and that each will be supported in his or her efforts to accomplish this goal.

• The teacher is responsible for creating an intellectual environment where serious mathematical thinking is the norm. More than just a physical setting with desks, bulletin boards, and posters, the classroom environment communicates subtle messages about what is valued in learning and doing mathematics.

• Effective teachers know how to support students without taking over the process of thinking for them.

(Principles and Standards for School Mathematics, 2000)

Supportive EnvironmentThe comments below were made by students on an anonymous end of year evaluation survey. What indicators lead you to think that this student was or was not in a supportive environment? Discuss your answer with your face partner.

Student A“I sometimes felt a little intimidated, and was not comfortable asking questions based on seeing the reaction of this teacher in responding to others’ questions. Not often, but certainly more than once in this course, I felt as though the teacher was a little short and impatient with students’ questions.”

Supportive EnvironmentWhat indicators lead you to think that this student was or was not in a supportive environment? Discuss your answer with your shoulder partner.

Student B• “I've learned so much about mathematics and myself in this course.

This course has helped me regain my confidence in math. As for myself, I've learned how to improve my patience while practicing problems and I've gained wisdom by appreciating my mathematical errors. Ms. XXXX has impacted my life mathematically by her passion for math and by her generosity.”

Multiple Opportunities

No matter how well you taught your lesson, students will still need practice, and lots of it! What types of practice do your students need? Quality not quantity!

Variety of WaysDifferentiation is…GAPSS Instruction Standard 2.2 –

… teachers making appropriate use of differentiation, including adjusting content, process, product, and learning environment based upon diagnosis of students’ readiness levels, learning styles, interests and personal goals.

• Example: Flexible grouping strategies; activities appealing to auditory, visual, and tactile-kinesthetic learners

• Non-example: Whole-group instruction all the time; teacher does most of the talking

Three Guiding Principles of Standards-Based Instruction

All students learn more when …• they have a clear vision of the learning target.• they meaningfully interact with the content in a

supportive environment.• given multiple opportunities to learn in a variety of

ways.

Fulton County Standards-Based Instruction Definition

Using a variety of resources to assess, plan and instruct in a way that encourages students to know what they are learning, why it is relevant, the ways to get there, when they have learned it, and how they can go even further.

1 Process and 5 Components of Standards-Based Instruction

Using a variety of resources to assess, plan and instruct in a way that encourages students to know what they are learning, why it is relevant, the ways to get there, when they have learned it, and how they can go even further.

Steps 2 Achieve Component of Standards-Based Instruction

Artifact or Evidence

What Standards, Essential Questions, Open-ended items; posted student work with commentary

Why Relevant and authentic tasks

Process Agendas, cooperative learning

When Formative assessment items and techniques; posted student work with commentary

Further Anchor and enrichment activities that connect topics to past and future learning

Steps 2 Achieve Process of Standards-Based Instruction

Artifact or Evidence

Assess - collect evidence indicating what your students know, understand, and can do

Warm-upsQuizzes, testsQuestioningPeer activitiesTicket out of the doorWorksheetsHomeworkProjectsVerbal assessmentLabsJournal writing

Steps 2 Achieve Process of Standards-Based Instruction

Artifact or Evidence

Plan - Line up what students will learn, how they will learn, and how they will know when they reach the learning goal

Lesson plans using the 7 steps of direct instruction:1. Communication of Learning Intentions2. Communication of Success Criteria3. Build Commitment and Engagement4. Teacher Presentation5. Guided Practice6. Summary7. Independent Practice

Steps 2 Achieve Process of Standards-Based Instruction

Artifact or Evidence

Instruct - Use different ways to involve students in work that will help them reach the learning goal

Sample student work from differentiated activities

FCS Lesson Plan Template7 Steps of Direct Instruction

Standards-based Instruction• Identify features of standards-based instruction in

Video Clip• Answer the following questions on your viewing

guide: Which of the three guiding principles or five components of SBI did you see in the video? Which ones did you not see?

Summary• How do the items on your Give One, Take One

handout relate to the 3 guiding principles or 5 components of standards-based instruction?

• Post-test: Anticipation Guide

Ticket Out the DoorWrite a sentence that begins with one of the following prompts:1. I now know that...2. I learned that...3. I was reminded of...4. I was surprised to learn that...5. I discovered...6. I've revisited an old idea about...7. I can explain that...8. It's amazing to know that...9. I will ponder on...10. I can connect this idea of....to....

Adapted from MentoringMinds.com