## Reflection: Developing a Conceptual Understanding Cooking with Mathmaster Chef (Day 2 of 4) - Section 2: Warm Up

My students have always come to me with prior experience with integers. This is not always a good thing. Many of them have memorized procedures, without conceptual understanding. Subtracting integers is a topic where I often experience this phenomena. I my school, the most prevalent procedure they recall from prior work is the "big plus sign" in which they change the subtraction of a negative number into a big plus sign. For my students, this creates several obstacles to using operations with integers successfully:

• My students are sometimes confused when asked to subtracting a signed positive integer.
• Some of my students habitually change the sign on all of the integers when they "add the opposite". Some consider arbitrary sign changes to be a possible problem solving method.
• My students often ignore the context of problems involving the subtraction of integers and they do not recognize obvious mistakes.
• I find that my students who "add the opposite" have more difficulty conceptualizing the multiplication of negative integers.

Unfortunately, students who learned to rely on a tried-and-true trick tend to rush forward with calculations when we arrive at this topic. It is a challenge to get some students to think about the meaning of the operations or to notice a mistake. For me, the key to overcoming this issue is to stop students and ask them to put their actions into context.

Today, I found it was really important to send the message to my students that they weren't done when they had an answer. They still had to explain it in relation to the context. For example, the vertical number line/thermometer was a really useful tool in helping them visualize a problem, because it gave them time to think (and a different perspective). It also gave my students another way of modeling a problem (other than a numerical expression). Since numerical expressions are often related to memorized tricks, using a different model often allowed students to think about the problems in a new way.

Developing a Conceptual Understanding: Avoid a rush to procedures

# Cooking with Mathmaster Chef (Day 2 of 4)

Unit 4: Operations with Integers
Lesson 2 of 24

## Big Idea: Students will see the relationship between integers and operations and will use multiple equivalent methods.

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Standards:
Subject(s):
Math, Integers, Number Sense and Operations, Operations and Expressions, temperature model, number line, multiple methods, conceptual development
54 minutes

### Erica Burnison

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