Growth Mindset

One of my favorite things to do with my students is celebrate their failures as well as their successes.  Sometimes, when we have worked on a really hard problem, I ask students to bring up a failed strategy to the front for us to talk about.  We all look at the failure and talk about what ideas and strategies the group got right inside the failure and what the failure taught us.  

We use stems like, "I noticed that..."  or "I wonder... were you thinking?"  

I try to encourage other students who did not participate on the "Epic Failure" to do the talking.  This engages students in each other's work and makes them analyze each other's thinking.  It places student knowledge at the center of the class, rather than teach knowledge and helps orient the kids toward one another.  It has really been a game changer having various students present and analyze other's work instead of their own.

I think a next step might be to have an "Epic Failure" wall where we place some of our favorite mistakes and celebrate what we learned from them.  My hope from all of this is that students (and myself) develop  a growth mindset where we try hard and scary things to push our learning further.  

This "Epic Failure Wall" will be part of my New Year's teaching goals. What is on your to do list?

The Problem with Memorizing Multiplication Facts: Number Sense

 When I first started teaching, my mentor teacher pulled out a sticker chart and showed me how she taught her students math facts.  Each week, on Fridays, she would set a timer for five minutes, ask the kids to put their pencils in the air and blast off to completing 100 problems.

If students reached 90 percent or high, then they moved on to the next set of multiplication facts.  Most of my kids memorized their facts.  The problem with this?  I am not sure I taught them enough number sense to go along with it.  

Sure, my third graders and I acted out multiplication problems and drew them.  We played games and cut out arrays, but I am not sure why I felt the need to place the timed test in front of them.  I wish I had got out counters more and played with the manipulatives.  I definitely did this when introducing division, but why didn't I do it more my first years when I was introducing multiplication?

Memorizing facts isn't enough to get them a mathematical understanding.  My kids needed to touch objects, build arrays, decompose arrays and observe how multiplication sentences can be decomposed and composed again.  If I had understood the distributive property more myself, I would have been better at educating my kids early on in my teaching career. 

Today, I definitely have manipulatives out and at the ready.  They are not in a closet collecting dust with my old worksheets from ten years ago.  They are in a place my kids can access and do access on a daily basis.  And I teach hard things.  My 3rd and fourth graders are studying volume, graphing ideas on a coordinate plane, completing algebraic equations and all the time they are touching manipulatives, exploring logical thinking and problem solving, trying new ideas out and sometimes failing.

I need to keep finding questions for my kids to explore to ignite their curiosity.  Finding the right open ended, manipulative friendly problem can be tricky when you have multiple learning styles and kids with various needs.  I continue to work on it. I am creating these and finding them and soon I will place them on TPT for others to use if they want.  

Cheers.  Bust out those manipulatives!!!

Open Math Problem Solving

 I decided this month that I am going to create open math problems for Teachers Pay Teachers, because they work fantastically with my gifted students. Open math problems are questions that have more than one right answer.  Therefore, my students can explore many solutions and can come up with ways to generate multiple solutions to a problem rather than one limited way.   

For example, rather than give my 4th graders the question: What is 25 X 17?  I ask them how many  ways can you solve 25 X 17?  

I then follow up with questions like:

• How can you represent that visually? 
• Can you create your own model?  
• How is this strategy connected to another strategy you used? 

Open problems, especially ones completed on white boards, lend students to push their thinking farther and give me avenues for higher level questioning.  Also, a bonus is that almost all my students can access the questions at some level but then its easy to give students a nudge farther along the continuum of understanding. 

Another open question I tried was one from Youcubed and mentioned again in the Building Thinking Classroom tasks.  It is the painted cube task that you can find here: Painted Cube.  In the problem, it asks if a 4 X 4 X 4 cube (made up of little cubes) was dipped in paint, how many smaller cubes would have 3 faces painted, 2 faces painted, 1 face painted and no faces painted.

I liked this problem because all my students were able access it and many of my students built the model with cubes in my classroom.  I was able to extend it for my gifted students fairly easily by asking what would happen in a 5 x 5 x 5 cube and a 6 x 6 x6 cube and then creating rules about the patterns. 

One key teaching technique that helped me was actually putting all their information into a graphic organizer, that I created   This organizer provided the structure around the patterns so we could have a math discussion about what we noticed and wondered.  We talked about why patterns emerged as well. 

As I reflect on this lesson, I am reminded of how graphic organizers, when used correctly, can aid in student understand and deepen thinking.  It can clarify ideas, solidify understandings and push kids to see things in new ways.  For example, my students noticed that there were always going to be 8 smaller squares that had three faces painted because there are always 8 corners on cubes and we were not changing the shape dipped in paint.  They found connections between the inner cubes with zero faces painted and the smaller cubes that they already examined.  It was a great activity and I highly recommend this one for anyone studying volume, geometry, and visual learning. 

I believe in the power of open questions, which is why I am going to create a resource for other people to explore.  Wish me luck on this crazy endeavor!

Vertical White Boards

One of the biggest teaching mistakes in my career was making my kids sit down during math time.

I always wondered, How do I keep little Kevin from throwing manipulatives? How do I help engage Jess and prevent her from pretending to be a cat during math?  Well, the answer, my friends, was just to have my kids stand up and work in partners during math at whiteboards.  

You see, I stumbled up on this little nugget of wisdom last year, when a friend (Thanks Ms. Bhatia!) recommended that I read Building Thinking Classrooms by Peter Liljedahl.  I am a single mom with little boys in select baseball and basketball, so I have precious little time.  

Luckily, this book was available on Audible and I just listened to it when I was driving into work. I committed to trying what I learned on my ride and over time, my math teaching got better and better because my students were thinking more and more.  

The beauty with vertical whiteboards are that the students can lean on each other when they need help.  They can "phone a friend" and get ideas from white boards near them.  Ayaan can ask his buddy Olive to explain his strategy and I can see where everyone is on a problem, by just glancing around the room.    

I use prompts to debrief like: 

"How is your strategy similar and different from Jenn's?"

"How did Francis solve this problem?"

"What did Frankie get right here, even though there is a piece that might not be right?" 

Even though this is my 19th year teaching (yikes, how has the time gone by so fast?!?!), I am going to be trying new ideas, messing up, learning things, and journeying in the classroom.  If you would like to following along and listen to what I have learned and created, join me as I play with math!

Click here for some problem solving math that can be done on Whiteboards.