Monday, March 4, 2024

Mind Shifts

We have spent the better part of a year looking at new curriculum resources that will best support our students to become the best mathematicians they can be.  

A few takeaways that have been identified or reinforced after looking at a variety:

Each curriculum says it is aligned with the CCSS and math teaching practices.

Each curriculum resource has good and bad pieces to it.  

If people just rely on the text in the teacher's manual to deliver instruction, they will not consistently be giving students what is best.  

Books are a RESOURCE. The standards and math teaching practices are what is best, and the book is just a sequence and guide.  Other resources should still be included. (Just because the book doesn't say to pull out a visual or manipulative doesn't mean you shouldn't...most students need these!)

Choosing the resource is not going to mean fabulous or not fabulous instruction. It is what is done with the resource that will make the instruction meaningful to students.

Math discourse does not just mean having students turn and talk more.

Pages of practice problems do not build problem-solvers.  They are not a necessary component of a curriculum resource.

3 Act Tasks are still important even though they are not included or referenced in most curriculums.

Students need time to make sense in their own way first.  Once they have an idea of where to go, they may change that as they discuss and listen to classmates.

Culture has to be built in a classroom.  It begins in August but is reinforced throughout the year and throughout all subjects.  Telling students to persevere in September does not mean they will be able to in April.  It needs to be part of every day with students.

Math should be an adventure--a combination of puzzles, games, practices, talking, and surprising connections that students make--not test scores.

The person delivering instruction still has to make the necessary shifts in their instruction in order to use a curriculum resource in a way that is fair and equitable to all students.  

Have you been through this process?  Have you found these to be true, too? Teaching shifts need to occur no matter what curriculum resource teachers use. 

Friday, August 11, 2023

A new puzzle to consider

Recently, a friend introduced me to this game/puzzle, and I wanted to be sure to share it with you.  It might be a great thing to use your PTO money or ask a generous parent to pick up for the class.

The only problem I really have with this game is its name: Genius Star.  I hate for that to cause students to believe they aren't capable of solving it, or vice-versa, that if they are able to solve it, it makes them a genius! 

This puzzle explores spatial relationships which for so many of our students can be a challenge.  It also offers students the opportunity to distinguish pieces they should prioritize as well as a trial in perseverance!

Here's how it works:

Roll the die that come with the game:

Lay the little white triangles onto the corresponding triangles on the board:

Now, I usually solve these on my own, and I don't recommend that it becomes a racing game, but students then take the 11 game pieces and place them on the board to cover in the star.

Students can compare their solutions to see what they did the same or different.

Students can also reflect on what made the puzzle challenging or easy. 

The box comes with two black trays to solve the puzzle on, but you could maybe get more than one game so that more students could work to solve. I find it quite fun, and it highlights the spatial skills of math.  The company makes other similar games that will show up when you follow the above link to this game.

Students can solve the puzzle in pairs and discuss their findings, they can investigate the dice and the regions of the board that each one covers, they could create their own puzzle numbers that they think are unsolvable and ask classmates to prove them wrong, they could create fractional questions about the puzzle or its pieces, or you could use two solutions for the same numbers as a same/different discussion. It seems to me like there are a lot of ways that this little puzzle could be used!

Let me know in the comments if you have found or find other ways to use this puzzle in the classroom!

Tuesday, April 18, 2023

Removing Ability Grouping while increasing Problem-Solving

One of the biggest missteps that occurs in math core instruction is people trying to organize it the same as they do their reading workshop.  

Traditionally in reading workshop, students are grouped by reading level and then called to the teacher to read and discuss a text at their level.  The teacher's small group instruction is really concentrated during this time when meeting with a small group of students away from the rest of their classmates.

In math workshop, we do not recommend this kind of grouping for students often.  In fact, through the work of Peter Liljedahl, more and more teachers are reading and using the research around VRG: Visibly Random Grouping. In his book, Building Thinking Classrooms in Mathematics, he explains how he realized students are more successful this way.

Visibly Random Grouping can be intimidating to some teachers because it means that they have to give up some of their control.  Not like let the room run crazy loss of control, but letting students work with whomever they match with.  Teachers have spent a lot of time organizing and reorganizing their groups for activities.  The thought of just letting it be random might be a lot.  However, once teachers begin to use VRG, they tend to love the results.

To begin with, the students should witness that the grouping has been random. There are apps that group students randomly(even Dojo), but you can always use playing cards, popsicle sticks, birthdays, or any other method that helps them see that you did not intentionally choose who was going to work together. Liljedahl's research shows that groups of 3 work best in most grades to get all students thinking.  In the primary grades, he recommends groups of 2.

Here are some of the benefits of VRG:

  • Increased engagement
  • Improved collaboration skills
  • Reliance of students on each other more than on the teacher
  • Improved student ability to work with anyone and recognize the strengths that classmates possess
  • Better flow of learning with students not just sharing in their group but also with others in the room: the feeling of being on the same team
  • Perception of the students that the teacher believes they can do it.  They don't have to be placed with a student who can "pull them along" or one that they need to support. No matter who they are with, they will be able to access the problem and move forward.
As teachers begin to move towards more use of VRG, they will find themselves removing labels from students.  This subtle shift in thinking will carry over into the students' views of each other, too.  This video by Jo Boaler offers somemre insight into the benefits of heterogenous grouping.

There are many teaching shifts that Liljedahl discusses in his book.  Visibly Random Grouping is one that is a great first shift for all teachers, and it will help when they decide to give a Thinking Classroom a try.

Tuesday, March 7, 2023

March is Full of Palindromes this Year!

 As we approach the end of March, we come close to multiple school days which are palindromes. From 3-20-23 to 3-29-23, our dates will be palindromes, and they may offer opportunities for you and your students to explore palindromes!

Students of all ages can look more closely at palindromes! I am going to focus on explorations with numbers, but your students might enjoy finding words that are palindromes, too. Here are a few books you might share with your students:

Some of your students may get caught up in noticing individual words that are palindromes, but some may enjoy the word play involved in sayings and phrases that are palindromes.  At either level, it is word work that many students find FUN!

For math explorations, you might not explain to your young students what a palindrome is, but let them discover!  

  • Using your pattern blocks as a visual, you can give students numbers to "create" and allow them to notice what makes these numbers special.  For example:

If you display the pattern blocks to represent different digits, then you can dictate numbers and ask students to create them.  Can they identify the pattern that makes palindromes special?  Can they see with the March dates how they are palindromes?

  • Ask your students to find all of the palindromes between 0 and 100.  What do they notice about two-digit palindromes? Is there a pattern in 3 digit palindromes?
  • Will there be other palindromes this year?  How about next year--What palindromes will there be?  Is there ever a year without a palindrome date?  What can your students find?
  • Finding palindromic numbers Math For Love has a great lesson exploration opportunity where students search for different levels of palindromes. It offers a way for students to add, look for patterns, and have fun with numbers--all in one activity!

I hope you and your students find some time to explore the fascinating patterns and elements of palindromes in our words and numbers!  You might want to consider ending with this Weird Al video, Bob, which is made entirely of palindromes.

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.