# App Review: Osmo Numbers #tmwyk

Since it was Christmas, and we finally had some free time, I decided to bust out something she had gotten earlier this month: Osmo Numbers.  I have a feeling that given the success of other Osmo products, the popularity of this one might surge.  We had tried Newton, Masterpiece, and Tangrams and kinda liked them.  I was hopeful.  Optimistic even.  (I think you see where this post is going).

Their contains the following video, which addresses math anxiety and illustrates the power of turning math into a game.

Here are some quotes from reviewers:

I couldn’t agree more:  we (educators and parents) create math anxiety in our students/children by insisting that math has one right answer. Often we convey that there is one right way to arrive at that answer as well. Consequently, children grow up believing math is about rules and procedures rather than creativity and exploration.

Reviewing the App

Description (from website): Kids arrange physical tiles, including dots and digits, to make numbers and complete levels. Add by putting more tiles, subtract by removing tiles and multiply by connecting tiles together. Experimenting becomes fast and intuitive.

The first section (Count) is decent.  Children have multiple dot tiles (like dice) that contain either 1, 2, or 5 dots.  They need to arrange tiles to total the numbers in the bubbles to make them pop.  It was interesting to me to see my daughter, Maria, make sums in different ways.

I was also intrigued that she always made numbers between 10 and 20 using two fives and then the remainder.

Things went downhill quickly.

In the “Add” section this is 1 + 4:

However, in the “Connect” section, this is 14:

Furthermore, in the “Multiply” section, this is 1 x 4:

Why is this a (HUGE) problem?  The design of each of these stages reinforces the belief that mathematics is about isolated rules rather than connected ideas.

That’s worth reiterating:  Math should be about connecting ideas and not about isolated rules.

The app boasts “when kids get the idea that there are multiple good ways to solve a problem, math becomes creative and fun.” I’m fighting my knee-jerk sarcastic-response mode big time in order to keep this professional.  All kids are really doing here is finding different ways to recall facts.  And as they progress through the app, the meanings of their representations change.  This doesn’t help build math confidence and break down math anxiety.  It sturdies the foundational thinking that math concepts don’t relate.

Here’s a great example of that.  Maria is frustrated that this doesn’t equal 10 like it did yesterday. But there isn’t anything to differentiate addition from multiplication besides the fact the tiny title (that she can’t read anyway) says so.

There is no visual representation of 5×5 being 25.  No arrays, no area models, no dots.

Why am I making this such a big deal?  This app, and many like it are being touted as game-changing, revolutionary, and brilliant. But when I search through the Osmo Makers page, I see no teachers.  In fact, I see five years of actual classroom experience, none of it in a public school and none math-specific.

I admire the goal to “revamp the unimaginative worksheet.” But I’d rather it replaced with a better worksheet than with something that tears down conceptual foundations of how numbers build and replaces it with fact-fluency.  Sorry, Osmo.  This product is a giant fail.  I’m returning to Talking Math with Kids where math doesn’t just claim to be creative. It actually is.

# Somewhere between Concrete Sequential and Abstract Random

It occurred to be relatively early in during the trimester this past fall that my college algebra students (generally) have no idea what I mean when I say “quadratic function.”  This isn’t because they have never heard it, learned it, or used it.  But that technical of a term simply has not stuck around in their long term memory.

So, similar to linear functions, we start with a pattern:

from youcubed.org and visualpatterns.org

I then had them make posters including how it is growing, what the 10th, 100th, 0th, and -1st cases would look like, table, graph, expression, and relationship to the pattern.  Instead of one large poster, they use 4 smaller pieces of paper and tape them together.  That way each group member can contribute simultaneously.

I noticed:

• It is difficult for students to describe how an irregular shape is growing.
• It is even more difficult for them to describe something abstract like the -1 case.
• Many of them expressed the overall growth as “exponential.”
• Most could easily see the two rectangles formed and determine the dimensions with respect to “n.”

I wondered:

• If they could connect the work with patterns to other quadratics.
• How to have a meaningful discussion around the “exponential growth” issue.

Their homework was to answer similar questions for this pattern from You Cubed’s Week of Inspirational Math:

Spoiler alert: the rule for the pattern is f(n) = (x + 1)^2 or f(n) = x^2 + 2x + 1

So where do we go from here, two days before Winter Break?  My goals are to review some specifics on quadratic functions and simultaneously help the students make connections between different representations.  I know what I must do.  I must channel my inner Triangleman.

[Backstory:  Christopher Danielson and I go way back. At least to 2014. Maybe even 2013.  Seriously though, I strive to organize my college algebra class the way Professor Danielson describes in his blog.  I have picked his brain on more than a few occasions and he is gracious enough to give me advice in certain curricular areas. In short, his philosophy titled “They’ll Need it for Calculus” is the foundation of my College Algebra course. ]

Ok, back to room C118.

Me: Write down everything you know about the function y = (x+1)^2

(Most write down the expanded form, some start to graph, but not many)

Me: What other ways can we represent this function?

Students: Tables! Graphs! Pictures! Words! Patterns! Licorice!

Me: Sweet!  Let’s do all of that, minus the Licorice.

(I give them a few minutes to create a table and a graph.)

Me: NOW, write down everything you know about this function.

I circulate and hand each group a half sheet of paper.

Me: Write down the most important thing on your groups list.

At first I wasn’t really concerned what exactly they wrote down, but how they defended their choice. Then I came across this in all of my classes:

We came up with a pleasing list of attributes of a positive parabola that included vertex placement, end behavior, leading coefficients, and rate of change.

Next up for discussion: Parabolas grow exponentially.

Me: Turn to your partner and tell them whether you agree or disagree with this statement and defend your choice.

Students: Yes, words, words, words.

Me: Ok, now the other partner, say how you know something grows exponentially.

Students: Multiplied every time, more words, blah blah blah.

So we agreed that 2, 4, 8, 16, 32, 64… is an example of something that grows exponentially.

Me: Numerically, how can we tell how something is growing?

Students: (eventually) Rate of Change!

We came up with this table and agreed that these two functions were definitely NOT growing in a similar way.

Now on to helping them understand what it means for something to grow quadratically…

# Making Groups Work

For about a year now, I’ve positioned my desks in groups of four. This trimester, my largest class is 35 students, but I was determined to make the groups fit.  I think I nailed it.

My room isn’t really this big. This is a panoramic photo.

For a lot of students, group work has consisted of a couple of things:

1. We compare answers, but  when in doubt, write down what the smart kid has.
2. We work in close proximity to one another, but for the most part, individually.

I’ve been reading Jo Boaler’s new book Mathematical Mindsets which address productive group work and have also read Strength in Numbers by Ilana Horn which surrounds similar issues. (Ilana has blogged on status in math class here) Both texts highlight the importance of addressing status in the mathematics classroom.  Because today was the first day of the new trimester, I thought it was a great opportunity to model and discuss what great group work looks like in order to level out the social status of students in my class.

1 – 100 Group Task (adapted from Sara Vanderwerf)

• Make sure students are in groups of 4.  Groups of 3 or less should join another group and partner with another member of that group.
• Give students highlighters or markers.  Make sure each group member has a different color.
• Distribute one handout per group face down.
• Have students decide who will go first and then continue in a clockwise direction.
• First student will highlight or cross off the number 1.  The next student will cross off number 2.  The following student 3 and so on.
• Give students a fixed amount of time (I did 2 minutes) to get as far as they can.

While students are feverishly crossing off numbers, discretely walk around and take pictures of each group as they work.  Be sure to capture models of group work you would like to highlight. For example, note students helping one another find numbers.  Also, include students all looking at the paper no matter whose desk it is on.

When time has elapsed, have groups make note of where they left off.  I asked, “if I had you discuss strategies, would you be able to improve the number you were able to cross off?”  Most will (obviously) agree, but then I give them a minute or two to examine their paper and discuss some strategies.  If your students are paying close enough attention, they should notice that the numbers are divided into quadrants.

Redistribute a new sheet, face down and start the time again for 2 minutes.  Again, circulate and take pictures, this time capturing the increased determination represented by putting their heads together and keeping the paper on one desk.  For fun you may want them to record their new number.  I had students record their number for the first round compared to the second round.  We then discussed how we could rank the groups based on the results which ended in a nice conversation about rate of change.  If I were more savvy, I might take the data from all three of my classes and put them on a scatterplot in Desmos to see if there is a relationship between their first round score and their second round score.  Alas, that was not to be.  Afterall, the purpose of the activity was not to “win.” It was to talk about what great group work looks like.

I revealed to them that while they were working I was taking pictures.  I had them predict what we would see on the pictures that would demonstrate a productive group.  We made sure to clarify that groups won’t always physically put their heads together to work. But that the idea of all group members focusing on the same task at hand was essential.  This allowed us to lay the foundation for future meaningful group work so that the students benefit from it.

Link to PDF of handouts

# TMC 2016 Proposals

We are starting to gear up for TMC16, which will be at Augsburg College in Minneapolis, MN (map is here) from July 16-19, 2016. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC16-1). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Saturday, July 16 and 48 one hour sessions that will be either Saturday, July 16, Sunday, July 17, or Monday, July 18). That means we are looking for somewhere around 70 sessions for TMC16.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 18, 2016 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Thank you for your interest!

Team TMC – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Cortni Muir, Jami Packer, Megan Schmidt, Sam Shah, Christopher Smith, and Glenn Waddell