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

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

3. 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

4. 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.

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

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

7. Poverty and performance

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

9. 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

10. 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?

11. Two Theories of Instruction

12. 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.

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

14. S4Y Suite of Assessments
CRA
Collaborative Study
Clinical Interview

15. 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.

16. Concrete Models

17. Representational Models

18. Abstract Models

19. 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?

20. Collaborative Study
John
Brianna

21. Clinical Interview Natasha

22. 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

23. Math for All Learners
Math for All Learners
K-2

24. 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

25. 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)

26. Menu
Problem
Skills work
Game
Reflection (Journal)

27. 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

28. 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

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

32. Illuminations

33. Illuminations

34. 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

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