Mathigon & Polypad & Puzzles...Oh My!

I have been a fan of Mathigon's Polypad for quite a while now, and have found many great ways for it to be used to help students build better mathematical understanding as well as to challenge their current understandings.

I want to share a few of the great resources available on Mathigon in hopes that you will find ways for them to work for you and your students!

The Multiplication by Heart cards (created by Math for Love) are great visual practice for students as they learn to understand and master their multiplication facts.  

Of course, I also enjoy the Tangram  Builder which is located in the Activities section.

Exploding Dots can also be found here.  If you have not spent time in the Exploding Dots world by James Tanton, do yourself and your students a favor!  It would make for a great exploration for your students.  The Exploding Dots experience on Mathigon is an extension of the actual website, but still one to get you thinking.

What really got my attention on Mathigon is its Polypad section!  It has so many unique manipulatives and tools to offer your students.

This polypad includes a balance scale and fraction bars. Each could be used separately.

Students can make music using these tools found in Polypad.

These Prime Factor Circles are a match to Prime Climb and can be decomposed (if composite) or combined as you wish to create new products.

This is just the tip of the iceberg in this fabulous site.  You can save and link activities that you make within the Polypad, but you can also use some of the many that are already prepared.  One last thing to explore is the Lessons tab.  Inside of there you will find your way to a variety of puzzles and explorations for you and your students.

Take the time for your students and yourself to explore this site.  You won't be disappointed!

Building Math Culture

 I often talk to teachers about the importance of building a learning culture in their classrooms.  It is so important that students feel safe and valued in their learning ideas.

Recently, I came upon this website, which gives tips and has videos to guide teachers and families in promoting a growth mindset in students.  I especially liked  the examples within the section on Celebrating Mistakes.

It reminded me of a teacher I recently listened to excitedly explain the building of culture in her classroom.  She talked about how she and her students cheer for each other's  mistakes, how students grow in their ability to talk about math through the constant exposure to thinking problems, and how her students love math time in the classroom.  There was no doubt that this excited teacher was talking from the positive experiences happening in her room, and that her students, too, had wonderful experiences as growing mathematicians!

Everyone in the room could feel the joy that this teacher exuded, and I'm sure, like me, they were wishing to have students (or be a student) who were a part of this classroom.  As students grow and content becomes more and more, I think teachers find it more difficult to create this type of atmosphere, but by visiting the website, teachers might find just the motivation to build a stronger classroom learning culture. Even in October it is not too late!

We are all math people!

Slowly, I am beginning to notice the phrase "math person" disappearing, and I am thrilled!  We are all math people. It is not a subject for the elite--all of our lives involve math.

As is often said, people rarely go around and say, "I can't read," yet they have no issues with stating that they can't do math. I believe that people say this because they limit their definition of math. Math is such an important piece of our everyday lives. 

Math is about way more than just computing.  It is about logic and thinking and patterns. It is about shapes and sounds and data. It is about puzzles and perseverance.  It is something we can all do.  It is something that all of our students can do.  It is just how this looks that may vary.

Computers were created by great thinkers so that we do not need to spend all of our time completing computation problems.  The part that we need to do (and our students need to do) is think about the math: What does this data tell us?  How can we use this data?  What do I need to do with these numbers? Which fraction is bigger? What fraction is smaller? What discount is better? Which measuring cup can I use when I can't find my half cup? About how much money will I need?  How is symmetry used in art? How does logic help me solve a Wordle?   This is real world math. This is math that matters to us.  Knowing that 7 x 9 is 63 is an important fact for sure, but it will only be relevant to a person as they age if it is necessary as part of their daily activities.  Many carpenters know their 12s times tables for this reason.

So many other beautiful things that we do and experience daily involve math like baking, building, music, and art. Once we expand our thinking around the definition, we will see that we are all math people.

A t-shirt that I have seen many times says this:

HOW TO BE A MATH PERSON:

1.  Do math. (any type)

2. Be a person.

The Value of Routines

Classrooms with strong routines reap many benefits.  This has become very evident this year as i have seen so many more classrooms begin math instruction each day with a routine.

In this year of continued chaos caused by the pandemic, teachers are finding that through routines, they can reinforce and review skills from previous grades.  They are also able to use routines to preview skills that might not be coming until later in the year.  So many free, well-designed routines are out there for teachers to use that it is easier than ever to find one that meets our students' needs.

Low-floor, high-ceiling routines are wonderful for engaging all students, and they usually involve a visual that helps students to all be able to "step-in" to the learning.  Favorite examples of these types of routines include Which One Doesn't Belong and Same/Different.  Teachers and students alike enjoy these routines because there are so many possibilities within one routine as they allow students to make sense of the problems in ways that make sense to them.

Many of the routines from Steve Wyborney are also loved by teachers and students.  These routines contain visuals, offer great exposure to vocabulary, and build number sense.  Teachers love them because they are professionally made and easy to use, and students love them because they are fun!  

Of course, Number Talks also are a routine that helps to build student discourse and fluency.  Using the book as a guide for these helps students to develop and use strategies when they are ready.  Doing Number Talks regularly has been shown to grow student fluency and flexibility in computation.

As students become more familiar with routines, there are many ways teachers can tweak the format.  For example, they might decide to have students create their own following a favorite routine.  (Creating your own Which One Doesn't Belong isn't as easy it might seem.)  Students can create these routines and share them with other classrooms besides their own giving them a larger audience for their work.  Teachers might also use routines as a daily warmup such as revealing one clue a day to an Estimystery and then discussing the students' thinking at the end of the week.  I've even seen teacher print out images from routines and have students discuss them as they wait outside of a special class like PE or music.  A routine image might be part of a weekly newsletter so that families can discuss it together.   There are many ways that these routines can be used throughout a day's learning in addition to a warmup for math block.

All of these math class routines help to build a strong classroom culture of open, flexible thinking.  They also strengthen students' number sense and confidence while expanding their math vocabulary.  Teachers gain better insight to student development and can use these routines to help determine what next steps to take instructionally. They see quickly how students grow through the use of routines that meet their student needs; the routines may change from year to year.  

Math routines help us to build mathematicians whose confidence help them to take on the math practice standards as part of who they are.