Developing Mathematical Practices July 16, 2017

First, let’s do some math With a partner: Using the colored squared build towers to represent these numbers 5, 7, 6, 10 Or, pass out the squares to each person with the first person receiving 5,…

Why groupwork? Intellectual goals: Conceptual learning Creative problem solving Developing academic language proficiency Social goals: Increasing trust and friendliness Working in a group transfer skills Increases student engagement

Which one doesn’t belong?

What makes a student mathematically proficient? NCTM VISION OF MATH AS MORE THAN PROCEDURES TO BE PRACTICED AND MEMORIZED Process of problem solving Reasoning Representations Communication Making connections From this vision came the 8 standards of mathematical practice

Update our beliefs about math Rediscover math content So, how do we get there? Update our beliefs about math Rediscover math content Modify our instruction to match our new beliefs and content understandings From Math in Practice

Update our beliefs about math adapted from Math in Practice I believed…. Practice makes perfect Mastering calculations is the ultimate goal of mathematics Math is about getting the right answer Math is a series of isolated skills You must know basic facts before you can learn to solve problems The first one finished wins The teacher tells students how to do math

Rediscover math content adapted from Math in Practice Most of us were not taught math for understanding We were taught to memorize rules Our students are being asked to model and discuss the rules

We can combat this attitude! Why change? We can combat this attitude!

Modifying our instruction adapted from math in practice Ask deep questions Build conceptual understanding BEFORE procedural fluency Make connections Rethink teaching problem solving Integrating problems into daily lessons Use multiple representations of mathematics Encourage student talk and writing Integrate assessment into instruction

When Tricks Should Not Be for kids Show a child some tricks and he will survive this week’s math lesson. Teach a child to think critically and his mind will thrive for a lifetime.

Tips, Tricks and strategies Look for key words Cross out non-essential information so that you are not distracted by it Draw a picture of each step of a problem ……….

Key words aren’t the key to understanding math Why don’t key words work? They don’t allow students to use what they already know to make sense of a situation Ie: There are 3 boxes of chicken nuggets on the table. Each box contains 6 chicken nuggets. How many chicken nuggets are there in all? “In all” signals students to add 6 and 3 Key words encourage students to take short cuts instead of making sense of the situation.

Irrelevant information Step by step illustrations To determine relevancy you need to be able to evaluate and analyze the information. To draw each step you nee to analyze and prioritize the information. These “tricks” require the very skills needed to solve the problem without the tricks or tips Only critical thinking and logical reasoning skills can help

Meaningful strategies that matter Pay attention to the units of measure Sally brought 7 cookies to share, and Suzy brought 5 cookies to share. There are 6 children in the class. How many cookies does each child get? Would it make sense to add 7 cookies + 5 cookies + 6 children What makes sense is (7cookies + 5 cookies/6 children)

Leave out the numbers There are days in Spring. If it rains days. How many days will be sunny?

Use reverse word problems to practice abstract thinking 7 + _____ = 10 Imagine the story that goes with the equation.

Let students do the thinking adapted from math in practice Organize classroom tasks to focus on discovery and insight rather than the teacher telling students how to do the math Use the right questions to stimulate and stretch students’ mathematical thinking Orchestrate problem-solving experiences that develop the thinking skills and dispositions of a problem solver

Discover vs being told Build 2 x 10 with base ten blocks 4 x 10 5 x 10 What do you notice? Why is it happening? Will it always work? How do you know?

Instead of 2 x 10 = 20 4 x 10 = 40 5 x 10 = 50 As you can see you just add a zero to the original number

Build an array out of 12 squares Arrays Build an array out of 12 squares How can you use repeated addition to find the total number of squares? Could you represent the total number of squares with a math equation?

Your turn Using one color build an array to show 5 x 6 Using two colors build arrays to show 5 x 3 5 x 4 5 x 2 5 x 1 5 x 5

Questions from math in practice What do you notice? Is there a relationship between the original rectangle and the two split rectangles? Is there a connection between the original equation and the two new equations? What do you notice about the products of the rectangles? Why is that?

Questions cont’d from math in practice How can we use math notation to show that 5 x 6 is the same as 5 x 3 and 5 x 3 5 x 6 = (5 x 3) + (5 x 3) Why do you think I used parentheses? Do you think this will always be true? Will the product always be the same when we split one of the factors? How could you use this idea to help you with 9 x 8 if you forgot? Does it matter which factor you break up?

Adding numbers – grade 3 Task Here is one way to add 55 and 58 55 +58 113

Adding 55 and 58 Here are some different ways to add 55 and 58 Adding 55 and 58 Here are some different ways to add 55 and 58. Some are correct and some are not. If you think it is correct circle the word correct. If you think it is incorrect circle incorrect. Tell why you believe as you do by explaining why it is correct or incorrect. A) Double 50 and then add 8 and 5 correct incorrect B) Start with 58 then add 50 then add 5 correct incorrect C) Double 58 then subtract 3 correct incorrect D) Start with 55 then add 60 then subtract 2 correct incorrect E) Add 5 and 8 then add 100 correct incorrect F) Add 50 and 60 then subtract 5 and subtract 2 correct incorrect

Fractions Complete the fraction Task of your choice. What confusion or errors do you think students might encounter? What questions or hints can you prepare to move students forward without giving too much information?

Or, see Developing the Mathematical Practices – Free Problem Resources in sched

Or, use the ca mathematics framework Instructional Strategies Chapter

Thank you for coming Suzanne Damm sdamm52@gmail.com This Photo by Unknown Author is licensed under CC BY-SA