Tuesday, November 29, 2022

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!

Thursday, October 13, 2022

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!

Tuesday, April 26, 2022

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:


1.  Do math. (any type)

2. Be a person.

Monday, January 31, 2022

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. 

Monday, May 10, 2021

Best Practices: Where can you grow?

 It has been a crazy, stressful year.  The good news is that the end is in sight for this school year.  And, while we may still live with some restrictions when our new year arrives next fall, we anticipate that many things will return to a more typical format for instruction.

So--let's look with next year in sight.  I know your summer is looking promising.  You can't wait to just relax and enjoy all that the world has to offer without the weight of instruction on your mind.  However--I imagine, like me, you find it difficult to totally turn off school.  Here are some things you might consider looking into to grow as a math teacher for next year.  Think about these best practices.  Which ones seem reasonable for you as you continue on your math journey?  You might choose two; you might choose seven.  Do what works for you.

Daily Routines:  Using the beginning moments of your workshop to get everyone thinking around an interesting problem is a great way to get the juices flowing!  I would definitely include traditional number talks in these routines, but there are so many others to consider.  Look for low floor/high ceiling routines that allow all students to enter into the problem and encourage creativity and fun for all.

More Manipulatives:  CRA Instruction "puts math in students' hands so they can understand it with their heads."  All students benefit from this type of instruction, but sadly, we tend to move away from it too quickly. It is one of the best ways for students to gain conceptual understanding of concepts.

Numberless Word Problems:  Key words are cancelled.  They are not a good instructional practice because they do not encourage good thinking from our students.  Taking some time to think around word problems that do not have numbers is a fabulous strategy for our students.  It not only shows the link between reading skills and math context, but it puts another tool in our students' toolboxes that they can use when they are confused by a word problem.  Remove the numbers!

Counting Collections:  The counting collections activity is way more complex than just counting, but it is also as simple as just counting.  The CGI approach is really working hard in this activity that I love to use from K to 5th!  (It could be used with older students, too!) It is an in-action practice of concrete, representational, and abstract.  This can be done by individuals or in pairs, but as always, the sharing at the end is where the real learning occurs!  You do not need anything fancy to count, so don't feel like this is something you have to go out and buy materials for.

More Visuals:  Math is visual.  Find ways to help students SEE the math in everything you do.  From representations during Number Talks to counting aloud visuals to the Same/Different routine to Prime Climb or Tiny Polka Dot, put the math out there in a way that students can engage with and understand.  Visuals help all students to engage and step-in to the lesson.

Three Act Tasks:  These offer such a good opportunity for our students to  make sense of math, and they do not follow the "I do, we do, you do" instructional format.  There are so many available to choose from.  The tab at the top of this blog is a rabbit hole that will take you to quite a few.  How can you be more intentional about using them next year?

Heterogeneous Grouping:  Tracking students is not an equitable practice.  All students need the opportunity to see and do high level tasks.  Let's not limit our students.  Be more intentional about grouping your students with students of varying strengths.  Don't underestimate what your students can do.

More Incorporation of Data:  Jo Boaler has added resources to her Youcubed website around data.  SlowRevealgraphs.com  has a number of prepared slide decks for many different levels.  These can be used in math class or incorporated into content areas.  Teaching our students how to read, question, interpret, and create various data representations is an important 21st century skill.

Desmos:  This platform offers so much for students, but also for teachers!  The platform is manageable and you can find a large number of ready-made activities that go beyond DOK 1 on this site.  I have many listed and aligned by standard in the Resources to support CCSS tab at the top of the page.

Weeks of Inspirational Math:  I have blogged about this more than a few times.  1st time   2nd time  3rd time  I love these!  I believe strongly you will, too, and so will your students.

Puzzles:  Our students do not have enough experience with persevering through challenging problems, and puzzles (both paper and tangible) give them experience with this skill.  Maybe you just add a jigsaw puzzle table next year, or maybe you take on KenKens--either way, your students will grow! (and probably have a little fun along the way)

Each year, we step into our classrooms with a fresh start and with plans of doing better than the year before.  By challenging yourself to grow in your math instruction, you will not only grow, but so will your students!  Good luck.

Monday, January 18, 2021

Removing Labels from Students

One thing that often challenges teachers is the way that they group students.  After working with students, they tend to have a group that they consider "low" and a group that they consider "high." Sometimes this designation comes as a result of testing.  This is an area where mindsets need to change.  When we think of students in these terms, we tend to determine their track and limit or expand our expectations--depending on the group.

I understand where this thinking comes from as it was taught to us as best practice for a while.  However, as Jo Boaler and other researchers point out, it is not what is in the best interests of our students as it pigeonholes them into believing that they are not good at math or that math should come easily to them.  Students who are consistently told that math comes easily to them often don't know what to do when it doesn't, and students who are led to believe that math is a struggle for them will want to avoid it because they are "no good" at it.  

So how do we correct this mindset?  There are a number of things that can be done.  First, we need to be very deliberate when referring to students.  We should work to no longer use terms like "high" or "low."  What I find is that most of our students have strengths and weaknesses.  Just because they have difficulty with computation doesn't mean that they don't have a great eye for geometric thinking.  

Secondly,  every effort should be made to not group our students every day by what we perceive to be their ability level.  Students should be heterogeneously grouped so that they can all benefit from hearing the ideas and thinking of others. (Imagine if your principal always grouped teachers according to the strong teachers and the weaker teachers.  How would the weaker teachers ever grow if they only had each other to get ideas from?  And how would the stronger teachers develop better understanding of their craft if they had no one to think deeply with? Everyone brings something to the table.)  Consider using visibly random grouping--an organizational structure researched, practiced, and  encouraged by Peter Liljedahl as helping students become better problem solvers.

Next, use low-floor/high ceiling problems as much as possible with your students.  From your opening routines to the rich tasks you ask your students to explore, find activities that all students can access and take to the level that they want.  These tasks encourage creative thinking and offer may opportunities for rich mathematical discourse.

Being intentional in making these changes will lead to greater learning from our students and improved equity for all.

Tuesday, December 8, 2020

How have you changed?

2020 has, in many ways, contained both stagnation and growth. The stagnation is what seems to resonate with us.  So much time at home, a limited circle of people to interact, and a school year that makes it challenging to see the desired growth in our students tend to overpower our thinking.  It is easy to focus on these things, as they are such a part of our daily lives right now.

However, there are also so many ways that we have grown in the last year. We have gained more time for self-reflection, had time to actually pursue our interests, become quite adept at Zoom meetings, and for many of us, learned how to celebrate holidays with a small circle rather than our large family gatherings.  While all of these opportunities have not been our choice, they have allowed us to look at our lives in a new light, and hopefully, there have been things we have done that we hope to continue well after this pandemic is in our rearview.

But as a math teacher, what changes have you made that you want to stick around?  Have you eliminated pages of repeated problems?  Have you put more time into the hows and whys of student work rather than the final results?  Has making math visual been a priority in your instruction? Have you been more intentional with your practices and built in routines that fit your students' needs?  Do your students see math as more than just computation? Have you offered more opportunities for creativity and critical thinking?  Does your classroom culture celebrate mistakes as steps toward growth?  

I am hopeful that some of these changes have occurred for you, and that you see the value in keeping these practices into the return of our post-pandemic world. While that world still may be many months away, these best practices are good now. Remote, hybird or in-person instruction.  Polish them up so that you have them in good shape for our return to "normal" instruction. Whenever (and whatever) that may be.