What's your next move?

Our presentation from Math in Action 2017

Description: 

Games are an effective way to engage students in learning. Participants will experience how to support the development of pre-adolescent mathematicians through purposeful play. [Grades 3-5]

Consider what you think it means to effectively teach mathematics. Now take the Simile Survey provided below. What are the characteristics of your simile selection that relate to good mathematics teaching?

A while back, Dr. Doug Fisher introduced me to another teaching simile: Teaching is like being an expert commentator. During the lesson, the teacher highlights important aspects of the "routine" that the student might otherwise overlook. In cases where the action moves too quick, the teacher might need to "rewind and show it in slow motion" in order to clarify some move. Here is an example from the 2016 U.S. Olympic Trials that demonstrates these characteristics. So what does this look like in math class?

Imagine we are in a 3rd-grade class playing BINGO. If the students are fluent in reading number symbols, there's not much to the game. So let's break it - add another dimension by allowing players to decompose the number that's called.

If you were in a 5th-grade class, they might ask why they can't decompose the called number into more than two addends ... or use operations other than addition. Then the challenge might be, "Can I get a BINGO with just one number called?"

After (or during the game), what sorts of things would you want the students to notice? What would you highlight and maybe have to slow down? It depends on the game and our players.

• If I was playing the regular game of BINGO with young kids still struggling with number recognition, I might be sure to call "thirteen" and highlight ways to tell the difference between 13 and 31.
• If we are decomposing, I might want kids to recognize that 38 can be decomposed into 30+8 or 31+7 and highlight the concept of compensation.
• For 5th graders, I might show how "thirteen" can be written as 13+8/(9-7)-4 and highlight an important property of zero in our number system. [To demonstrate another important property of zero, ask students if they could cover the entire board if "thirteen" was called.]

It is important that teachers have the opportunity to play games before using them with their students. That way the teachers can consider possible modifications (ways to "break" the game) that would meet their students' needs. It also gives them experience playing the games that can lead to insights into important mathematical aspects encountered while playing that the teachers might want to highlight for their students.

Game Centers 

Number and Operations - Fractions 

Grades 3-5 

• Fraction Go Fish 
• Fraction Memory [pdf] 
• Cookie Fractions [page36]
• DecimalPickle 
• Pattern Block Fraction Game
• Fraction Track [app]

=====

Other Game Resources

• Adventures with Mathematics [MCTM]
• Gameswith Fraction Strips and Fraction Cards
• Rational Number Resources [NRICH]
• Investigations Games

=====

After playing the games, we reflect on our experiences using Math Teacher Chair:

• What games did you play?
• So what mathematical ideas would you want to highlight?
• Now what would you do to break the game or slow down the play so students would benefit mathematically from playing?

Thanks for your participation. You can reach us using the following contact information. 

"Rocket science is child's play compared to understanding child's play."

~ Unknown

If you are attending the upcoming 2017 NCTM Annual Meeting and Exposition in San Antonio, we will be presenting this session again. 

We promise it will be better next time thanks to the feedback you've provided on your session evaluations (or in the comments below).

Where do you stand on teaching mathematics?

Today my Teaching and Learning Middle Grades Mathematics course begins their unit on teaching mathematics. This follows units on doing mathematics and learning mathematics. We begin this unit by taking a simile survey that asks respondents to complete the following:

Ideally, a mathematics teacher is like a(n):

a. Coach

b. Doctor

c. Entertainer

d. Gardener

e. News Broadcaster

f. Orchestra Conductor

• Choose the simile that you believe best describes a mathematics teacher and explain your choice.
• Choose the simile that does the worst job of describing a mathematics teacher and explain your choice.
• Is there another simile that does a better job than these of describing a mathematics teacher? If there is, then what is it and what makes it better than these?

This survey follows similar simile surveys done for doing and learning mathematics. The doing mathematics unit had integers as one of the topics, so I asked my learners to rate the "doing" similes from -5 (the worst) to 5 (the best). We created a life-sized number line as a way to share and compare our choices. 

Rational number was the mathematical focus in the learning unit. For this survey, learners assigned their worst "learning" simile a 1 and then decided how many times better each other simile was than the worst one. The life-sized number line went from 0 to 1 this time. Learners computed the following ratio for each simile: simile rating to best simile rating. (i.e. The best simile was a one.) Again, we shared and compared our choices by standing on the number line.

The teaching mathematics unit concentrates on geometry. Today, I will ask them to stand in one of four corners representing strongly agree, agree, disagree, or strongly disagree for each simile. It is certainly a simpler process than the others but it often results in some interesting discussions.

Ideally, a mathematics teacher is like an entertainer. Where do you stand?

What does a mathematics learner look like?

Today my Teaching and Learning Middle Grades Mathematics course ends a unit on learning mathematics. This follows a unit on doing mathematics. At the beginning of this unit, we took a simile survey that asked respondents to complete the following:

Ideally, a mathematics learner is like a(n):

a. Inventor

b. Sponge

c. Mechanic

d. Computer

e. Reporter

f. Explorer

• Choose the simile that you believe best describes a mathematics learner and explain your choice.
• Choose the simile that does the worst job of describing a mathematics learner and explain your choice.
• Is there another simile that does a better job than these of describing a mathematics learner? If there is, then what is it and what makes it better than these?

This survey is based on an instrument I used in my doctoral research to measure beliefs about doing, learning, and teaching mathematics.

How would you complete this simile survey?

What does it mean to do mathematics?

My MTH 329 class just finished the first unit of Teaching and Learning Middle Grades Mathematics. The focus of this unit is on the NCTM Process Standards. Yesterday we spent a considerable amount of our class period reflecting on what we’ve been doing so far.

We start the workshop with a schema activation/connection that asks the learners to review a simile survey taken the first day of class. One part of the survey says, “Choose the simile that best describes doing math and explain your choice.” The similes to choose from are: climbing a mountain, conducting an experiment, cooking a meal, reading a book, working a puzzle, or playing a game. In reviewing their original choices, I want my learners to consider how their view of doing math has changed and why.

The focus/concentration for the workshop is to create an anchor chart representing what they think it means to do mathematics. This chart might hang in their future classroom as a constant reminder to their learners what it means to be a mathematician. (My colleague shares his experience with anchor charts here.)

During the activity/construction phase of the workshop, groups of four work together to develop a rough draft anchor chart. The first group builds on the simile idea and develops a chart showing doing math as working a puzzle. Each piece of the puzzle represents a different aspect of their vision of doing math.

Group two decides that they want to make a chart that would appeal to middle grade learners. They use graffiti as the theme and begin searching Urban Dictionary for terms they could use for the Process Standards. At one point they discuss whether or not the chart is appropriate (culturally sensitive) and decide that it is because it is intended to engage and not to mock.

The final group considers the anchor chart from a graph theory perspective. They had just been discussing a discrete mathematics assignment and it seems to find its way into the representation. That’s the Green Arrow up in the Algebra block. The color of each arrow has some significance, I think. (These are works in progress.)

These are rough drafts that I post on our classroom Blackboard site. The future teachers will make adjustments to whichever one they choose and make it their own for inclusion in the course portfolio. This is the reflection/consolidation portion of the workshop.

So what do I think it means to do mathematics? It involves collaborating with others in an effort to solve problems, making and revising representations for/of our thinking, trying to connect various ideas, and communicating the reasoning behind our thought process to others. In other words, yesterday doing mathematics involved making anchor charts.