#CSandMath: Partnering Math and Computer Science

csandmathIn the last year my amazing colleague Ashley and I have been working to find ways to make learning math interdisciplinary and engaging, while also preparing students for a future that has many potential opportunities in computing.  One of the projects that has come out of this work is what we’re calling #CSandMath, which somewhat obviously promotes a partnership between computer science and math 🙂  It hasn’t been easy work.  

low floor high ceiling

(Image retrieved from: http://wcsumathcoach.blogspot.com/2015/11/low-floor-high-ceiling-math-coach.html  Thanks WCSU for this awesome visual)

We want to create scenarios that are low floor, high ceiling and promote critical thinking with an easy entry point, yet unbounded potential.  To be sure, we’re not trying to replace wisdom of mathematical structure with a technological tool.  Instead we’re trying to teach kids how to use their understanding and harness it with programming in a way that is meaningful.  We hope that students see math as essential is attacking problems with computational thinking.

So here is an example of a lesson I’ll be using on Friday with my 8th grade students who have mostly mastered graphing and rearranging linear equations.  It will hopefully bring them back to how we started the entire unit on graphing with a table, and we will try to put some real life twists on the finished program as you’ll see in the GIF’s at the end of the lesson.  Sorry for the poor clarity on those, but to help you decipher, the green Tonka truck starts 3 feet away from the wall and you can time the feet per second.  The room is 30 feet long.  The cherry tomato in the wine glass has an initial weight of 7.7 oz and each addition weighs about .2 oz.

slope intercept

Graphing Slope Intercept: #CSandMath Lesson

I’m begging you to try it even if you have little to no programming experience!  Try it yourself and then with your students 🙂  How would you make it better?  Do you think it has value?

If linear equations don’t have a place, you could easily adapt the lesson to other families of functions.  Or if you wanted a just show them how to program one of their formulas, this structure and lesson linked below has worked well for us.

Programming any formula

Programming any Formula in Scratch Lesson



Trimming the Fat

Trimming the Fat

It’s interesting that I’m choosing to start this conversation based on a book that I read a few months back and continue to revisit called Essentialism.  This book was recommended by an exceptional colleague of mine, Boyd Weiger, as well as one of my favorite math leaders, Robert Kaplinksy (post here).  By page five, author Greg McKeown shines light on the mantra that has begun to act as my personal mission: Less but better.  When I run a personal audit on myself, it is glaringly clear that I have changes to make both in how I choose to spend the time that comprises my life and which priorities are king.


This notion applies as much to our curriculum in math as does to how I spend my own time.  I’ve been lucky be a part of some difficult work in our district around setting priority standards using different lens such as longevity of skills for lifelong success and readiness for future achievement in course scope and sequence.  For example, here is an somewhat dated list of the 10 standards we chose as the priority for our 8th grade students.  Ten.  Now I realize that those standards can unpack into various skills, but are we guilty of overdoing it?  Are we making a problem that doesn’t need to exist?  Take a look at how IXL unpacks Minnesota’s 8th grade math standards.  By doing all of this unpacking (and typically testing) we are usually missing the opportunities to explore the concepts in an authentic way, play with their potential, and apply to areas relevant to kids.  Below is a quote I’ve been sharing in every opportunity I have to present.

Invent to Learn

For my personal growth I have found this to be wholeheartedly true, and I didn’t have to pick up any new math skills to have extraordinarily powerful learning moments.  Our units should involve hands on projects and certainly interdisciplinary connections foundational to a STEAM mindset.  There are so many amazing PBL lessons and opportunities to integrate other disciplines like computer science and makerspace design that the kids deserve.  In other words, what I’m trying to say is…

Make Math Great Again

What about you? Are you already doing it?  Please share your ideas, results, or opinion 🙂




Math > Computation

You’d think as a 10th year teacher this revelation that math is so much more than computation would have come to me sooner, but it has taken a lot of experience and pondering over other’s work for the ideas that follow to congeal.  More specifically, I’ve come to realize the extent to which I undervalue, under validate, and under assess the structures and understandings outside the realm of calculating in my classroom.

It was Conrad Wolfram’s TED Talk, Teaching Kids Real Math with Computers, that first had me pondering with one of his opening questions; What is math?  Conrad WolframHe explains that to him, math encompasses the four areas pictured here and we should focus student’s time on the three areas that stress thinking, while partnering computers in the computation process.  As with most published work, I do not completely agree with all of his points the same as most would not agree with all of mine.  However, his viewpoint has had a tremendous impact on me, and I have returned to watch this talk many times.

I personally like the classic framework written in 1957 by George Polya in How to Solve It: A New Aspect of Mathematical Method of understanding the problem, devising a plan, executing the plan, and verification.  Polya 4 Step Problem SolvingThis classic four stage approach does miss the idea of posing the right questions in the first place, but provides a valuable look into where to validate student work in critical thinking and problem solving.  I do, however, think this iterative process can be effective on more than just math applications where an answer is calculated.


Towards the end of last school year I began to evaluate the exams we were giving students more closely due to the realization of how much weight we were putting on them in terms of their overall grade.  For instance, I’ve taken a screenshot of the firstpage of an area assessment that we give to our geometry students that accounts for 80% of their grade in that unit (along with other similar assessments).  Area TestNow questions certainly do get progressively harder, I just didn’t want to share the entire test as most teachers are still using the problems.  What I found was eye-opening.  Of the 25 total points, 23 of them were aimed directly at computation.  That’s 92%.  And the question I had to ask myself is, “Is that ok”?  Is the calculation of the area even what’s most important to me as the teacher in this unit?  The answer for me is no.  So I began to ponder what was the most important aspect of this unit from my viewpoint and why?  What I realized after this reflection was that I valued student understanding of the structure of area beginning with the rectangle and deriving all area formulas out from it.

“Interesting,” I thought to myself.  I actually value the structure and progression of the formula derivations the most.  As I was scrolling through Ed Southall’s (@Solvemymaths and author of Yes, but Why) Twitter posts earlier this month I came across this threadabout people’s most unexpected wow moments in math, which is definitely worth your time to read.  Within it I found that educator Howie Hua found this area progression to be his biggest epiphany moment in his math experiences to date!  Area Deriving RectangleWhat if I better structured the unit so students were able to experience that progression, while also valuing and validating it in the end of unit assessment 🙂

Last year I asked students to write a Scratch program that explained one of the formula derivations.  Unfortunately, I only allotted one 48 minute class period to do so, but was impressed by what many were able to accomplish in that amount of time.  One studentfocused in on the trapezoid, and described what it meant quite eloquently.  I only awarded him five practice points… #undervalued:(trapezoid


This year I have the ability to change that.  The ability to validate this creative thought on a much larger scale.  I can have the students express each derivation in a way that’s unique to them and let the full progression unfold and be part of their performance grade.  I can add value to analysis, planning, and reflection in a way that I haven’t yet done.

What about you?  What percentage of your grades are assessment based?  What percentage of those assessments are computation based?  Are the grades you’re awarding a true representation of student’s “mathematical” knowledge?



Math out of Bounds -> Bounds of out Math -> “BOOM”

A look into the name of this blog that I hope to develop in the coming years…

I didn’t attend this delivered message from Christopher Danielson (Find what you love.  Do more of that.), but I had a related epiphany elsewhere in the state of Minnesota.  It was a moment when I realized that I loved math beyond the confines of ”normality”; the beauty behind it’s possibilities, the creativity in its application, and the looming opportunities it holds in bringing value to the world.  Interestingly, it was the NOVA documentary, Fractals: Hunting the Hidden Dimension, that released in me this previously dormant part of my identity.  Here is a Twitter post from 2016 reminiscing the moment …(although I didn’t watch it in 2008, it was actually 2012)

love your math fractals
Before that point in time, I had always been an explorer in other areas of my life, but not in my classroom.  I was rigid.  I was focused on efficacy as it pertains to test scores and used them almost exclusively to critique my teaching.  There was something in this documentary’s message that opened my eyes to the notion that math is more than a set of sequenced skills, and that is was much bigger than I had ever realized from my previous experiences as a student or teacher.

It led me to spend relentless hours investigating more robust ways to discover and explore mathematics including Desmos, Geogebra, and my current passion of teaching kids how to partner computer science with mathematics (see #CSandMath ).  It was a catalyst for me to begin looking for math in non-traditional school settings such as solving Rubik’s Cubes, coordinate geometry in The Math Behind the Movies (and other insightful connections from Pixar in a Box; See Environmental Modeling Here), and largely to the realization that math is a lot more than just calculation.  It’s creative, artistic, social, etc.  Mathematical makerspaces should be more prevalent in our schools don’t you think?

The slogan “Math out of Bounds” came to me in July of 2015 in a Fablab training program I underwent, where I began to see applications of “making” mathematics I had never considered before.  I decided to flip that mantra to “Bounds of out Math” which was more symbolic of it’s meaning to me and also created the acronym BOOM.  So behind the title of my blog and Twitter handle is a belief that most math classrooms in this moment are too bounded;  Too focused on the accumulation of skills, while leaving inventive thinking as a trait of unequal importance.  

Lastly, when I look at my beliefs and my own classroom practices I too often feel convicted.  I preach about this different kind of math, yet constantly revert back to old practices of direct instruction.  So I’m going to commit more deeply in 2018.  I’m going to fight the social pressure to capitulate to traditional methods because I believe it’s what’s best for kids.  Hopefully, I can influence some others to jump with me…