Math for Struggling Learners Helping All Children to be Successful with Mathematics

Why is math important? Access to math means access to college

Why is math important? Math builds “Human Capital” The skills learned in certain math classes are essential for being a productive employee Good math instruction teaches heuristic thinking Math classes “signal” high intellectual capacity In both cases, more math is looked at positively by employers

Why do students struggle? They have cognitive challenges that make learning math more difficult. They have received instruction that didn’t serve them. Curriculum or pedagogy didn’t build on prior experience Instruction was focused on learning pre-packaged strategies.

Who are Struggling Math Learners? Demographic factors Cognitive Factors Instructional casualty

Demographic factors are closely associated with math performance Socioeconomic status English language proficiency Race Ethnicity

Poverty and performance

The discrepancy between the performance of students based on race and ethnicity is referred to as “The Achievement Gap”. (NAEP, 1991)

Why do students struggle? Most often… Because they are forced memorize procedures rather than actually do mathematics Which means… Rather than work to develop understanding, students are taught to parrot the teacher’s understanding

Think of a student What do they struggle with? What remediation is available to them? What systems are in place to support students with occasional difficulties? What systems are in place to support students with significant needs? How are struggling students provided with specialized instruction?

Two Theories of Instruction

Math Instruction for Conceptual Understanding Students need tools to think with Students must get “stuck” in the right place and use tools Students experience mathematical insight. Insight is refined through the use of reflection and practice.

Sergio What does Sergio know about place value? Where might he have difficulty? What questions would you want to ask him?

S4Y Suite of Assessments CRA Collaborative Study Clinical Interview

Worms Dion is getting ready to go fishing with friends. Dion digs for worms in some dirt. Dion finds 53 worms and puts them in a can. Then Dion finds 5 worms under a rock and puts them in the can. Dion thinks that is enough worms to go fishing. Dion counts all the worms in the can. What number will Dion use to tell how many worms are in the can? Show all your mathematical thinking.

Concrete Models

Representational Models

Abstract Models

CRA Concrete: When Jimmy left for school in the morning he had 6 stickers in his sticker book. At school his teacher gave him some more stickers. When he got home he had 14 stickers in his book. How many stickers did Jimmy have that morning? Representational: Jenny counted 7 stickers in her sticker book. Her mom gave her some more stickers. Jenny now has 12 stickers in her sticker book. How many stickers did Jenny get from her mom? Abstract: Johnny had 5 stickers in his sticker book. He got some more stickers. Jenny now has 11 stickers in his sticker book. How many stickers did Johnny get?

Collaborative Study John Brianna

Clinical Interview Natasha https://mathreasoninginventory.com/Home/VideoLibrary

Conduct Collaborative Study Higher Performance for All Students Menu or Math Workshop Remediation Plan Clinical Interview Classroom Data Menu item Exit slip Journal prompt Sorting/Analyzing Conduct Collaborative Study Menu or Math Workshop Flexible Interview Classroom Data Menu item Exit slip Journal prompt Sorting/Analyzing CRA Assessment

Math for All Learners Math for All Learners K-2

High Leverage Standards K-2 Kindergarten All students will demonstrate: Counting to 20 Cardinality One-to-one correspondence Comparing quantities   Grade Two Adding and subtracting 3-digit numbers with consistency and accuracy (standard algorithm not necessary) Grade One All students will demonstrate: Knowledge of number values and sequence to 120 (cross century, cross decade) Knowledge of place value when adding and subtracting numbers within 120

High Leverage Standards 3-5 Grade Three All students will demonstrate: The ability to multiply and divide numbers within 100 (in context and in equations)   Grade Five The ability to perform all four operations with fractions solving accurately from both word problems and equations (using no standard algorithm; using modeling only)  Grade Four All students will demonstrate: The ability to multiply and divide any 2 numbers (in context and in equations)

Menu Problem Skills work Game Reflection (Journal)

Problem Offer a problem directly related to the lesson At different levels Offer a problem for review Offer a problem to gather data on upcoming content

Exemplars Exemplars is a new (old?) resource that provides: Rich CCSS aligned problems Potential solutions/strategies Differentiated Versions of the same problem Scoring rubrics Student samples

Skills Work Often this comes from elements of the program “Work Journal” “Practice Book” “Number Corner” “Math Boxes” Time for Differentiated arithmetic Practice

Illuminations

Illuminations

Math Journals Allows for multiple points of entry Provides the opportunity for students to learn by answering the question, and the teacher to learn about each student from the attempt, Requires more than just remembering a fact or reproducing a skill Provides opportunities for students to represent their mathematical ideas using models and written language, Provides opportunities for students to justify their reasoning and evaluate the reasoning of others

Now Try it for Yourself Problem Skills work Game Reflection (Journal)