How Do I Change Math Class Tomorrow?

As Dan Meyer put it, “math class needs a makeover.”  It breaks my heart to hear students say things like, “I’m not good at math” or “I hate math!”

In my opinion, one of the first things that needs to change is the focus on correct answers and the need for speed.  This leads students to believe that the only way to be good at math is to be right (quickly).  The other practice that needs to be eliminated is the language we use as teachers such as “that’s right” or “you’re so smart.”  

You’re So Smart

You’re so smart is one of the most damaging things you can say to a child.  What is smart?  What do we value and what are we showing them that we value?  Being smart needs to mean learning as a means in itself.  Or rather, the journey of learning.  This is not fixed but ever-evolving as we seek out and synthesize new information.  

As a parent, I have been guilty of this.  I’ll blame it on ignorance, but the truth is I kept it up for years as a teacher and a mother.  I knew the words tasted sour in my mouth, but they continued to come out and I continued to damage my child’s self-worth.  Harsh?  It’s true.  

Here is an example:

My oldest son started the district gifted program as a first grader. I was so proud!  From the time he was born, I had told him how smart he was.  He had finally been classified by the school system in the same way.  My job was done.  From that day on, his life would be rainbows and butterflies.

The reality was that from that day on, he began to feel even more isolated.  He went on to the full-time gifted program in sixth grade and I ended up pulling him out.  His stress level was through the roof, he was failing ALL of his classes, our family time was dominated by reprimands of his failure to finish his homework (which was unending), and the school’s solution to the problem was to medicate him.  We had failed him.  We taught him that learning was about homework and work completion  and not about creativity and problem solving.  The other message we sent was one of conformity; You must fit it in this box to be “smart” or successful.

He told me a few years later that he felt like the test had been wrong, that they made a mistake.  He wasn’t gifted.  He went on to say that he felt pressure to always have the answers and when he didn’t his failure was paramount.  Teachers expected more of him ALL THE TIME and living up to that expectation was stifling.  I had taught him and the label had taught him that intelligence was fixed.  We told him he was special, but not in a growth sort of way.  He had already arrived at being “smart” and now he would have to maintain the title.  

Luckily, my second child was eight years after my first and my message as a parent is vastly different.  I praise reflection and strategy and kindness and determination.  I allowed him to be tested (telling myself that I could better understand his needs if I did, a lie to be sure).  I realized that I had some lingering pridefulness attached to the label that I am still working out.

However, this time, when I presented it to him, I framed it very differently than I did with my first.  I told him that there was a school with additional opportunities for learning that he might enjoy.  I let him choose whether or not he wished to attend.  He attended in second grade and decided to not attend this year.  

My message to parents is now this: if you want to compliment your child academically, focus on effort and inquiry.  Say things like, “wow, I can tell you really worked hard on that,” or “I love hearing about all the new things you are learning, I can tell how much you it.”

You’re Right

“You’re right” takes all of the learning away from the student and places the teacher in the seat of a referee.  Student work becomes not a creative endeavor, but a race to impress the teacher.  The focus is taken off of learning and put on performance (which is what is done when training circus animals).  

If we really want students to be problem solvers, we need to ask the right questions and probe for understanding.  Students need to own their solutions and the first way to do that is to change our language as teachers.  Guided Math in Action has a great list of prompts for students to use to prove their solutions..  It is one of my favorite to use with students, and illustrates how to help students own their own learning and be confident in their solutions.

I have a couple of examples I would like to share about this topic.  One comes from my own child who is now a high school Junior (the one referenced above).  I can pinpoint the day he first viewed himself as a failure in math.  It was third grade and his teacher was a wonderful lady who was energetic and nurturing.  She had been teaching for almost thirty years and all the students loved her.  She (like many still do) believed that the best way to master multiplication facts was to put students through a battery of timed tests.  She had a cute little board that she used to keep track of their progress where they would build their ice cream sundae as they completed their facts.  I always knew when it was a testing day, because my son would come home with a look of failure on his face.  Math was no longer about creativity for him, it was about being fast and being right.  He did not perform well under time constraints and though his idea of fun in the car was to practice multiplication problems and discuss his creative strategy for solving them, it had lost its luster once he was asked to do it quickly.  He has taken Algebra 3 times and finally passed this year due to a teacher who really understood his learning style.  He hates math and instead of wanting to pursue a career in astro-physics or chemistry like he previously had dreamed of, he decided that he was too bad at math to go into those fields.

Another example can be provided by a seventh grade girl who I have been tutoring for about a year and a half.  She was failing sixth grade math and had severe anxiety about it.  The first time we met, I gave her an assessment on number sense.  She would quickly (very quickly) give me an answer in a very fast, short response, then look at me in terror and say, “is that right?”  I knew immediately that this girl did not struggle with math, she struggled with confidence due to the experiences she had been provided.  We quickly came to an understanding, one that students know well.  “I don’t care how fast you come to a solution as long as you can walk me through your strategy and prove it.”  I have had the exact same experience with every student I tutor.  They are terrified of being wrong, and they have no way of proving they are right because that has never been the focus of instruction.  She now has a B in math and no longer looks at me to determine if the solution is correct.  

Lessons Learned

What I have learned, thanks to many phenomenal authors and researchers and my experience teaching diverse learners, is that all students have individual strengths and passions and they all deserve diverse learning experiences in math and outside of math.

Perhaps we need to quit asking all students to “master every standard” and agree on a set of skills required to be contributing members of society and then let students find their passion and develop it.  We need to remove the labels and focus on the individual.  I do still believe that students need to be exposed to new ideas and problems so that they can find their passions, but asking them to master every concept is no longer something that our world requires of them and perhaps never did.

I will end with this, it is my belief that the most powerful thing we can do for a child is teach them how to learn.

A Few of the Resources That Have Helped Shape My Beliefs

Mathematical Mindsets

Mindset

Number Talks

Teaching Number in the Classroom

Guided Math in Action

Dan Meyer

Jo Boaler

Twitter – #Elemmathchat

 

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3 Act Task: The Package Problem

We have had a question we have used for years in Title One Math that continually stumps students in division situations because of the context of the problem.  It is an excellent way to get students to think about the remainder in a division problem as it applies to different situations.  We lovingly refer to this as the package problem.  The question is, I have 34 cupcakes. They are packaged in packages of 6.  How many packages will I need?

When I was making and packaging my annual Christmas pretzels this year, I took a few pictures and thought this might be an excellent example of the package problem.

There are many different scenarios for this task which is what I think makes a really rich task.  You can ask, “How many packages of three will I be able to give out as presents?” or “The pretzels are packaged in packages of 3.  How many packages will I need to package all of the pretzels?”  The first question ignores the remainder because it is irrelevant to the situation.  The second question requires students to look at the remainder as a necessary part of the problem, but allows them to recognize that the last package will not be complete.  If I pair the first question with a third question, “How many will not be packaged?” attention is called to the remainder and can lead to a discussion such as, “Why did I make 2 extra?” or “How would I package them if I wanted to give a bag to each of 6 friends?” or “If I didn’t want to have any pretzels remaining, how could I package them?

Problem solving is all about context.  In my opinion, the reason students don’t do well with word problems is because they are not exposed to multiple contexts in mathematics when skills are taught in isolation.  Hence, the power of 3 Act Math Tasks (thanks Mr. Meyer).  I hope you enjoy this task and would love your feedback as always!

When I was taking pictures for this task, I was elbows deep in melted chocolate so I forgot to take some of the pictures I needed for the different contexts.  My plan is to make another batch soon and add those:)  So for now, I have the third act addressing the first question.

I’ve added a link on the 3 Act main page of my site to the google folder with all of my tasks, videos and pictures.  That way you can choose the pics you’d like. I love to use Nearpod for my 3 Act Tasks when I teach for the awesome opportunities for student input and data analysis:)  However, every time I run a Nearpod session it breaks the link to my blog, so I thought Google might be a better way to share these:)

Act 1: 

IMG_9263.JPG

What do you notice?  What do you wonder?

How many packages will I need for the rest of the pretzels?  Write a too high and a too low estimate.

Act 2:

act-2-pretzel-1Act 2 Pretzel 2.png

There are 26 pretzels.  Pretzels are packaged in bags of three. (Insert preferred question here) Act 3 addresses the question, “How many packages of 3 will I be able to give out as presents?” (Students might count the one package that is already shown in the picture and come up with 9)

Act 3:

Act 3.1.png

or this depending on whether they count the first package in Act 1.

Act 3.2.png

Extensions:

How would I package them if I wanted to give a bag to each of 6 friends?” or “If I didn’t want to have any pretzels remaining, how could I package them?

Personalized Learning Paths

I have been working on a project for quite a while to better personalize learning for our students in numeracy.  My teaching partner and I began one for literacy as well, but have a lot of work to do (I’ll blog about that when we are closer).  We are using the same idea for our other standards through the lens of our inquiry units, so those will also be rolling out as we complete them.

Our first grade students are 1:1 with Chromebooks in our classroom and we have spent countless hours and days and months now trying to decide how to best use these tools to boost student engagement and learning experiences(see the upcoming post about student scheduling to learn more about this).  We departmentalize for small group and teach all of the math lessons and two of our reading groups, while my co-teacher teaches most of our reading groups.

We have an amazing classroom space, 1:1 technology, and a great collaborative relationship between my co-teacher and I. However, we do face other hurtles such as limited storage space and trying to balance the usage of tech vs. hands on tasks.

We knew we wanted a way for students to track their learning that would allow for them to move freely from one standard to the next unencumbered by the learning paths of other students.  However, finding a mode of delivery that would allow for this has proven to be quite challenging.  In the end, you will see that we had to do some site-smashing to best meet our goal (and we hope it works).

What We Needed

  • Students to be able to track their standards met
  • Students to be able to access modules and activities for standards currently being practiced quickly and easily
  • Ability to link to websites for practice
  • Ability to provide modules that would not allow students to “fall down a rabbit hole” after completion
  • Ability for students to upload multiple types of assignements such as pictures of hands-on activity completed and assessment videos

What We’ve Tried and Why They Don’t Work Alone

Our district uses Canvas as our LMS and we love it for many of it’s features, most notably what we believe it was created for, a way to organize learning.  However, there are many other apps and sites that better meet the needs of emerging and non-readers and writers that are more user friendly for modules, online student assignments, direct instruction videos, interactive games and quizzes.

For modules, we used Canvas but were having trouble with the microphone. We talked to our Blended Learning Specialist and looked deeply at Canvas modules, but there are problems with the microphone that weren’t easily resolved and it was much more work for students to submit items than we thought reasonable.  We didn’t want them spending their learning time on accessing and uploading their assignments, we wanted them spending their time on constructing new knowledge.

We used Nearpod for whole-group modules, but we didn’t see a way for it to be used for students to work at their own pace.

We began by embedding our activities in Blendspace because of it’s icon-centric design, but found that it was too distracting for students when navigating because of the option to move to other activities on the pages they were accessing.  We also had a problem with some videos continuing to play while others started.  We had the same problem with YouTube videos because when the video stopped, they had the option to click on other videos and fall down the rabbit hole of “other videos you might like.”

We loved Vimeo for uploading flipped videos because it is a secure stand-alone program that allowed us to upload only that particular video.  However, Vimeo, like many other programs, costs money and we were soon reaching our storage limit.  We loved Screencast-omatic for recording flipped videos that captured onscreen material but then had to upload them to YouTube which led us back to the YouTube problem. We recently learned that it also offers storage for flipping videos of the same sort and it looks like it offers much more storage without distractions at the end.

We loved Seesaw as our online learning journal, but there is was no way to link it to our Canvas pages for content areas without them having to navigate the feed.

We loved Google Classroom for assignments and the quick add feature in the extension for classroom for sites.  We also loved the option in assignments to create a student copy automatically (and save to their drive), but assignments cannot be made for individual students or student groups.

However, our problem remained.  We needed a quick and easy way for students to navigate directly to their standard of practice and have quick access to the activities, but also have a way to track their progress and move along a continuum.

The Plan

standard-1We revisited Nearpod as they have recently added a student-paced lesson component that allows students to work through modules on their own.  We decided the options in Nearpod to add videos, activities, upload files and allow students to write on them and the different options for quizzes at the end would be the best fit for our learning modules at this age.

We decided probably the best thing we had seen to create these tracking sheets for the standards was to use Google Slides and share it with students through Google Classroom.  That way they could start at the task they needed to practice and work their way through.  We linked the Nearpod modules to the Google Slides as well as the other activities they needed to create and each one ended with an assessment of the standard such as uploading a video to Seesaw of them counting from 1-120 starting at different numbers.task-1

Our next issue was that while Seesaw is awesome, it only stays loaded on iPads and each student has to re-scan the code every 15 minutes on their Chromebook to add items from it.  Since most of our iPads are in use for OSMO in our classroom, we needed a way for students to have easy access to their stories so we printed a class QR code for each student’s clipboard and used shipping tape to tape them to the back.  Students always have their clipboards with them because they use them for their daily schedules and Lexia/Dreambox goal tracking.

We are still working through how to best store the hands-on activities for easy access for students, but think we may have some ideas on that as well.

Above are examples of a Domain tracking sheet and a task sheet for an individual standard.  The idea is for students to move the green smiley face over when the task is completed.  We will then meet check the Seesaw feed and meet with them to fill in the date met or provide additional instruction if it is not met.

We will begin using this tracking system first for numeracy in the next few weeks, so look for my reflection coming soon!  We are excited to see how it plays out in the classroom!

As always, please provide comments and feedback as this is a continual process for us and we need all the input we can get!

 

 

Adaptive Software Lessons

Our district adopted Lexia and Dreambox for our adaptive learning software for literacy and numeracy.  We noticed quite quickly after the start of the year that many of our students were putting in the “minutes” on their adaptive learning software, but they weren’t actually completing many lessons.  We talked to our district math coordinator and he said students should be completing 5 or more lessons each week in each program.

We sat with students and looked at their progress, had conversations about when to ask for help, started a parking lot where they could write their names when they needed help, discussed a peer help system for asking another student for help and tried motivators such as leader boards, etc.  Nothing was working.

We decided to try a new idea.  We created this goal tracking sheet for students to track goal-sheetstheir goals each week on a daily basis.  When they completed a lesson, they colored in a spot on their grid (this also helps with their math standard for bar graphs).  We told them that they would receive a Classroom Dojo point for getting all 5 lessons in Dreambox and another for completing all 5 in Lexia.  The kicker was that every lesson above and beyond 5 got them a Dojo point for each lesson!

In our classroom, we use Dojo as our reward system and do it a little differently than most.  We don’t believe in extrinsic rewards that lead to “junk” such as candy and toys; we want our students to be intrinsically motivated.  However, we also believe that students should have the opportunity to earn rewards for a job well done.  So we allow students to accumulate their points.   They can turn in 25 points for tickets such as “Lunch with the teacher,” “Bring a furry friend,” “Preferred seating (this is a bean bag),” etc.  The students can also save for backpacks or lunch boxes as we had many donated from an area business.  My co-teacher and I decided early on that we would give out Dojo points liberally if students were doing things that promoted growth socially or academically so we were both okay with giving these extra points each week as a motivator.

The results the first week were great!  Students brought their computers to us to check to see if their lessons matched ours and gave themselves Dojo points.  The ones who did not meet their goals, had a clear goal during make-up time so they could move on to STEAM stations.  This week was a short week back and we did not pass out our goal sheets.  We had several students ask when we would be getting our Lexia and Dreambox goal sheets.  We are excited to see this process and determine if it continues to be motivational for our students!

3 Act: Christmas Treats – Division 2.0

This task can be used two different ways.  It is designed to show the reciprocity between multiplication and division.  This post will lay it out as a division problem. The standard that this best addresses is 3.OA.A.2.  The previous post laid out a similar multiplication problem with a single digit divisor and dividend.

Act 1: 

IMG_9256.JPG

What did you notice?  What do you wonder?

How many columns of 8 will fit on the pan?

Give a too low estimate and a too high estimate.

Act 2:

Act 1 Division.png

What do you know?  What do you need to know?

Act 3:

IMG_9259.JPG

Extension:

I am packaging these in packages of 8 for gifts.  How many packages will I need?

3 Act: Christmas Treats – Multiplication

This task can be used two different ways.  It is designed to show the reciprocity between multiplication and division.  This post will lay it out as a multiplication problem. The standard that this best addresses is 3.OA.A.3.  The next post will lay out a similar division problem.  I have also included an additional image to extend the task using a 2-digit divisor (this is the context used for the division situation in the next post so don’t use it if you also want to use the next post in a division context).

Act 1: 

What did you notice?  What do you wonder?

How many treats can be made on the pan?

Give a too low estimate and a too high estimate.

Act 2:

Act 2- Christmas Treats.png

What do you know?  What do you need to know?

6 rows of 9 treats

Act 3:

Extension:

How many can be made using two pans?

Or try this one:

IMG_9258.JPG

3 Act: Melt My Heart

While recycling crayons for Christmas presents for our first graders, it occurred to me that this would be an excellent 3 Act Math task.  I decided to go about this one a little differently and used the video as the Act 2 and a picture for Act 3.  This activity provides an opportunity for many extensions!  Feel free to comment (as always) and let me know how it can be improved!

Although there are many standards that this task addresses, I feel it is a great extension to 3.OA.A.1.

Act 1:

What do you notice? What do you wonder?

Act 2: 

What do you know?  What do you need to know to solve your question?

11 crayons per heart, 6 hearts altogether.

Act 3: 

act-3-melt-my-heart

Extension:

What if I had 28 students in my class?  How many crayons would I need to make one heart per person?

What if the crayons were worn down to half of their full size?