My kids can : making math accessible to all learners, K–5

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couldn’t figure out why. Davel did not reason, he proceeded mechanically and did
not understand the meaning of the steps he took.
How can we help students link procedural and conceptual knowledge? What
explicit teaching supports students’ understanding of key mathematical ideas and
gives them tools to reason through problems? I have grappled with these questions
for many years and have come to realize that for me, explicit teaching involves
particular teaching moves designed to help students become active learners:
learners who engage in the process of thinking and reasoning through problems.
These teaching moves include asking students to:



  • elaborate their answers and explain why their solutions worked

  • think about what they know before solving a new problem

  • make connections among problem-solving strategies

  • make connections among representations: drawings, numbers, contexts,
    and concrete materials

  • work through their errors and misunderstandings with teacher support

  • reflect on their learning


In this essay, I discuss a selection of lessons in which I used these teaching
moves with a group of six fourth-grade students who struggled in math. These stu-
dents joined me every day for an hour during their math period. Their teacher and
I agreed that learning in a small group would help them move forward. Some were
English language learners and some were on IEPs or were referred for special ed-
ucation services. Part of my work with them focused on multiplication and divi-
sion, topics they specifically identified as being difficult.


Setting Goals for My Students


During my observations of the students, I noticed that, for the most part, they
used repeated addition or skip counting to solve multiplication problems. They
were not very comfortable working with arrays^1 and had a difficult time memoriz-
ing the multiplication facts. My intent was to help them understand the rela-
tionship between skip counting, repeated addition, and multiplication. I also
wanted them to become very familiar with the array model as a tool to help them
think through multiplication, and the distributive property in particular. My goal
was to help students develop these understandings, so that they would be able to
find the product of factor pairs they couldn’t remember and they would develop
reliable strategies to solve multiplication problems. Finally, I wanted them to be
able to make sense of division story problems.


MAKINGMATHEMATICSEXPLICIT

(^1) An array is an area model for multiplication that consists of arrangement of objects, pictures, or
numbers in rows and columns. See Figure 1–1, page 8, for an example.

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