Planning Effective Mathematics Instruction in a Variety of Educational Environments David Allsopp, Ph.D. University of South Florida Allsopp, Kyger, and.

Planning Effective Mathematics Instruction in a Variety of Educational Environments

David Allsopp, Ph.D.University of South Florida

Allsopp, Kyger, and Lovin (2007). Teaching Mathematics Meaningfully. Paul H. Brookes Publishing.

D. Allsopp

Essential Questions

• What is the target mathematics concept?• What did I learn from my mathematics dynamic

assessment (or other pre-unit assessment)• What is my instructional hypothesis (what students

know, don’t know, and why)• How do students think about these ideas differently

from adults and how can I use this information to inform instruction?

• How will I differentiate the instructional needs of my students?


Essential Questions

• What authentic contexts will I use?• How will I introduce/model the target concept to the

whole class?• How will I differentiate the

instructional/scaffolding/extension (generalization and adaption) needs of my students?

• How will I provide practice opportunities that promote proficiency/maintenance?

• How will I evaluate my students’ learning and determine the effectiveness of my instruction?


Planning for Responsive Mathematics Instruction

• Consider what students know, don’t know, and why• Consider stages of learning• Determine differentiated instruction needs/objectives• Select authentic contexts• Plan whole class instruction• Plan differentiated instruction• Plan practice opportunities• Plan how you will evaluate learning and your

instruction


Adapted from: Allsopp, D., Teaching Mathematics Meaningfully, 2007

Making mathematics

accessible through responsive teaching

Understanding & teachingThe big ideas in math ANDThe big ideas for DOING math

Understanding learning characteristics/ barriers

for students with difficulties In mathematics

Continuously assessing learningTo make informed instructional

decisions

Model for Meaningful Mathematics Instruction

Big Ideas of Mathematics~Number & Operations~Algebra~Geometry~Measurement~Data analysis & probability

Processes for Doing Mathematics~Problem Solving~Reasoning & Proof~Connections~Communications~Representation

Responsive Teaching Framework for Differentiating Mathematics Instruction

Core Instruction:• The areas to be studied in mathematics from pre-kindergarten through

eighth grade should be streamlined

• Proficiency with whole numbers, fractions, and certain aspects of geometry and measurement are the foundations for algebra.

• Conceptual understanding, computational and procedural fluency, and problem solving skills are equally important and mutually reinforce each other.

• Students should develop immediate recall of arithmetic facts to free the "working memory" for solving more complex problems.

What we know…National Math Panel

Adding it Up, National Research Council, p. 117, 2007

In order for students tobe successful in mathematics, each of these intertwined strands must work together.

How programs are designed is critical!

-Spiral vs. Strand design

-Traditional vs. Explicit

-Use of scaffolding to increase mastery & generalization of skills/strategies vs. demonstrate & replicate

-Prior knowledge: Instruction in related vocabulary and review of mastered prerequisite skills vs. assumption of prior knowledge

-Examples & non-examples

-Sequencing of skills (macro/micro)

-Progress monitoring vs. “wait and see”

Time to Reflect…

Individual Think-WriteWhat are some of the characteristics of my core math program?

Mix and Match 2

Summarizing CRA Results

Based on C-R-A Assessment Mrs. Carsen concludes students:

o Have difficulty representing fractions that are >, <, or = using unlike denominators

o Have difficulty determining >, <, or = using symbols between fractions with unlike denominators (abstract, representational)

o Have some ability to do this with fractions that have natural relationships (1/2 and 2/4, 4/6 and 2/3-abstract)

o Have difficulty relating written fractions to drawings(Lack concept of the meaning of a fraction)

o Difficulty with concept of “equivalent area” of whole to part when drawing

MDAResults

Hypothesis

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Instructional HypothesisWhat’s it all about?

Provides you with a focused approach to teaching that specifically addresses the needs of your students based on the results of a mathematics dynamic assessment.

Instructional Hypothesis

Context:

What Students Can Do:

What Students Can’t Do:

Reason:

“Given _____________________,

Students can _______________

Students cannot _____________

Because ____________________”Keep It Simple!

Given two fractions…

Students are able to…determine >, <, and = when fractions have like denominators at concrete, representational and abstract levels.

Students are unable to…determine >, <, and = when fractions have unlike denominators at concrete, representational and abstract levels.

…becausethey lack understanding of the area that fractions represent

Instructional Hypothesis

MDAResults

Hypothesis

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Given a set of 2 fractions, the majority of my students can determine >, <, and = when fractions have like denominators at the C R & A levels; however they cannotdetermine >, <, and = when fractions have unlike denominators because they lackunderstanding of the area that fractions represent.

Consider Stages of Learning:A Framework for Understanding How Struggling Learners Learn

Entrylevel

Acquisition Proficiency Maintenance Generalization AdaptionInitial Advanced

Accuracy

Rate

Retention

Stages of Learning

ExtensionTo focus instruction, it is important to know at what stage of learning students are with respect to the target math concept/skill…

Planning for Responsive Mathematics Instruction Determine

differentiated instructional

needs/objectives



Determine differentiated instructional

needs/objectives


Planning for Responsive Mathematics InstructionSelect Authentic

ContextPlan whole class

instruction


Planning for Responsive Mathematics InstructionPlan differentiated instruction

Plan practice opportunities



Plan evaluation of learning and instruction

Plan practice opportunities



Plan evaluation of learning and instruction



Plan differentiated instruction


Planning for Specific Learning Barriers of Students


Planning Effective Mathematics Instruction in a Variety of Educational Environments David Allsopp, Ph.D. University of South Florida Allsopp, Kyger, and.

Documents

teaching mathematics

mathematics accessible

instruction allsopp

big ideas of mathematics

mathematics dynamic

target mathematics concept

core instruction

class instruction plan