22 Oct Articulate how teaching and teachers create opportunities for success for some students and failure for others
Written answers have to be a minimum of 3 sentences.
Link slide 3:
https://youtu.be/X18cQkKMlhs
https://youtu.be/6VliMWIi9z0
Link slide 5:
Link slide 11:
Article found in last three screenshots.
Slides to answer to:
5,7,13,14,16,17,19
Module 9 Talk Moves
Due October 24, 2022, 11:59 PM
Course and Module Objectives
In this assignment, you will explore the following:
Course Objectives
CO4: Facilitate meaningful mathematical discourse.
CO5: Develop multiple strategies to solve mathematics problems.
CO8: Articulate how teaching and teachers create opportunities for success for some students and failure for others.
Module Objectives
MO1: Use sentence starters to facilitate mathematical discussions. (CO4)
MO2: Use talk moves to facilitate a mathematical discussion. (CO4, CO5)
MO3: Use various strategies to solve mathematics problems. (CO5)
MO4: Critique the use of timed tests in the mathematics classroom and suggest alternatives. (CO8)
Mathematics Content
Exploring Number Talks Introduction to PBA # 3 – 15 minutes
Multiplication Tables – 20 minutes
Strategies for Solving Multiplication Problems – 15 minutes
Partial Products and the Standard Algorithm – 15 minutes
Total predicted time to complete Part Two of the assignment
1 hour and 30 minutes
1. Number Talks
We are going to explore number talks more here. Number talks are a common method used in elementary math classes to build students’ mental computation skills and conceptual understanding.
Watch the first 5 minutes of the first video to see how this teacher introduces number talks to her students for the first time. Note that the teacher does not solicit all answers first (as is usually done). After the teacher gets the answer 10 from Tyler, it would be helpful to ask if any students got any other answers. Then she can ask, “Who would like to share their thinking?”
Watch the number talk on the bottom. This teacher solicits a wide range of answers, and then at the end she asks students who would want to change their thinking. Another approach she might consider at the end is to say, “We have lots of different answers over here. Who would like to make an argument defending one of these answers?” Then she wouldn’t have to go through each student getting them to revise their thinking.
On the next slide, describe 3 ideas these videos gave you about how a number talk should look in a classroom.
Answer the question based on the videos from the previous slide.
Describe 3 ideas these videos gave you about how a number talk should look in a classroom. Be as specific as possible and give examples that refer back to the video.
Type your response here.
1. Multiplication Tables
Rote memorization of facts is not as helpful as having a flexible understanding of numbers and being able to derive facts. Graham Fletcher is a well-known elementary educator. Watch him describe a revised approach to thinking about memorizing facts.
Teachers have many tools for building fluency in multiplication.
– Number Talks play a critical role.
– Games like “ How Close to 100?” and Pepperoni Pizza are helpful and low pressure. But what about the infamous flash cards?
– Flash cards that build understanding ( here and here) can be helpful (this is the kind of numerical fluency we want).
Memorization of multiplication facts plays a prominent role in the elementary curriculum. However, there is plenty of research showing that rote memorization of facts is not as helpful as having a flexible understanding of numbers and being able to derive facts.
Games Imagine laying several cards on the table (like the six to the right) and having students find cards that represent the same number.
Answer the questions below based on the material from the previous slide.
Memorizing multiplication tables is usually considered the main goal of third grade math.
How did the information on the previous slide change your thoughts about the traditional approach to memorizing multiplication tables?
How might an approach focused more on understanding have helped you as a student?
What might you do differently when you are a teacher from traditional memorization?
2. Strategies for Multiplication
See the methods students often develop for solving mathematics problems.
Study these examples, and then, apply what you learned to solve the given problems.
Complete Number Strategies for Multiplication
Examples of Complete Number Strategies
Before students are ready to break apart one number in the problem, they consider each number just as it is (that’s why it’s called a Complete Number Strategy).
These students typically use strategies based on repeated addition
The approach is generally not very efficient (particularly with large numbers).
Consider 63 x 5.
Complete Number Strategy: students use the number just as it is
These students typically use strategies based on repeated addition
The approach is not very efficient
Partitioning Strategies for Multiplication
Examples of Partitioning Strategies
This requires an understanding of place value – seeing 268 as 200 + 60 + 8 or 2 one hundreds, 6 tens, and 8 ones. This is an important step in developing an algorithm.
Students begin to break apart one number (and later both numbers) in a problem.
This requires an understanding of place value – seeing 268 as 200 + 60 + 8 This approach is relatively efficient
Partial Products Strategy for Multiplication
The links below show Examples of Partial Products. Watch each video until you are comfortable with the method.
Example One: 37 x 26 (There are several examples. Once you are comfortable with the method, move on to the next video.)
Try your own
Consider 37 x 26.
When you use partial products, you rewrite both numbers like this
(30 + 7) x (20 + 6)
This problem needs to be solved using the distributive property twice.
2. Partial Products and the Standard Algorithm
On a piece of paper, solve 24 x 38 using the following methods:
1) Partial Products LINK# 1 LINK # 2
2) the Standard Algorithm
Attach a picture of your work on the next slide.
Then answer the questions that follow.
Copy your work from the previous slide.
THINK MATHEMATICALLY Examine your work on the previous slide and answer the following questions.
What similarities and differences do you see between partial products and the standard algorithm?
Type your response here.
How will learning partial products first, help students make sense of (or understand) the standard algorithm instead of just following a procedure that makes little to no sense?
Type your response here.
Equity and Inclusion
Quotation on Math
Faster Isn’t Smarter
1. Read the excerpt on the left and answer the question to the right.
. . . I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Even when I was the first to answer the teacher's questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who weren't as good as I was answered before me. Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. Not only did I believe I was stupid, but I couldn't understand the contradiction between this stupidity and my good grades. I never talked about this to anyone, but I always felt convinced that my imposture would someday be revealed: the whole world and myself would finally see that what looked like intelligence was really just an illusion. If this ever happened, apparently no one noticed it, and I’m still just as slow. (…) At the end of the eleventh grade, I took the measure of the situation, and came to the conclusion that rapidity doesn't have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.
What stands out to you about this quotation and why? Do you relate to what the author is saying? How so?
Type your response here.
1. Read the excerpt on the left and answer the question to the right.
. . . I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent. And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully. Even when I was the first to answer the teacher's questions, I knew it was because they happened to be questions to which I already knew the answer. But if a new question arose, usually students who weren't as good as I was answered before me. Towards the end of the eleventh grade, I secretly thought of myself as stupid. I worried about this for a long time. Not only did I believe I was stupid, but I couldn't understand the contradiction between this stupidity and my good grades. I never talked about this to anyone, but I always felt convinced that my imposture would someday be revealed: the whole world and myself would finally see that what looked like intelligence was really just an illusion. If this ever happened, apparently no one noticed it, and I’m still just as slow. (…) At the end of the eleventh grade, I took the measure of the situation, and concluded that rapidity doesn't have a precise relation to intelligence. What is important is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't relevant.
What stands out to you about this quotation and why? Do you relate to what the author is saying? How so?
Type your response here.
2. Faster Isn’t Smarter
1. Read the article, Faster Isn’t Smarter by Cathy Seeley (She is a former President of the National Council of Teachers of Mathematics.)
2. After reading the short article write your answer to these questions on the next slide,
What types of timed tests do you remember taking in elementary school? How did taking these timed tests make you feel?
Imagine you are teaching third grade and trying to decide whether to give timed tests on students’ multiplication facts. What do you think you will do and why?
Answer the question about the article on the previous slide.
What issues or challenges does this message raise for you?
In what ways do you agree with or disagree with the main points of the message?
How did your thinking change after you read this article? (explain how you felt about what is discussed before reading the article and after)
Type your response here.
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