09 Dec Making Math Social: How a non-mathematician became excited about Math
How Much Does A 100×100 In-N-Out Cheeseburger Cost?
An introduction to the mathematical and pedagogical genius of Robert Kaplinski, http://robertkaplinsky.com/
I was introduced to math’ and pedagogy genius Robert Kaplinski’s work by the equally brilliant Crystal Kirsch at Tustin USD, CA in October last year. What first struck me about Robert’s site was that his beliefs were so perfectly aligned with the Verso message.
“The group is smarter than the smartest person in the group. When professionals collaborate, the work they do together is better than the work they would have done on their own. Sharing lessons and experiences with others helps us all become stronger.”
Robert focuses on the Why. He cites Carol Dweck and the importance of growth over fixed mindsets and he believes that teachers “must have rigorous expectations for how students should be able to express their math knowledge” in line with the requirements of the Australian Curriculum and US Common Core State Standards.
“What matters most is the question, ‘Is the student perplexed?’ Our goal is to induce in the student a perplexed, curious state, a question in her head that math can help answer.”
A believer in the importance of cultivating curiosity, Kaplinski puts forward 10 design principals for engaging math classes. Again, the importance of quality questions, perplexity, rigor and deep student engagement sits well alongside our Verso messaging. Similarly his focus on the use of real world images and video, planning for the transition of students from surface to deep, and making learning social ring a whole heap of Verso bells.
“Make math social. More engaging than having a student guess whether or not the ball goes in is showing her how all of her classmates guessed also. Summarize the class’ aggregate responses with a bar chart. Students will enjoy seeing each others’ short answers and opinions but we can also use the same social interactions to engage them in pure math.”
Robert Kaplinski’s website shares practical resources for teachers, along with a fantastic Problem-Based Lesson Search Engine which searches a range of carefully curated math’ sites (listed below) to help you find a problem-based lesson
As a non-mathematician, what excites me about Robert’s website is his generously shared series of lessons. Searchable by grade level, I found myself reaching for a pen and paper to attempt to answer several of the real world problems presented on the page. I found that I was inspired to have a go. I was perplexed, curious and, at times frustrated, but I never thought I would spend a night in a hotel room cozying up to a bunch of middle school math problems! These are great.
I had the opportunity to try one of Robert’s activities out with a class in two Grade 9 and 10 Algebra classes.
I took my lead from Robert’s inspirational plan and then following some discussion, the students engaged with the following Verso provocation. (Available in the Verso global library)
In and Out Burgers
Honors Algebra Grade 9
Common Core Standard: Math.HSF-LE.A.2
In-N-Out ordinarily sells hamburgers, cheeseburgers, and Double-Doubles (two beef patties and two slices of cheese). While they don’t advertise it, they have a secret menu which includes a burger where you can order as many extra beef patties and cheese slices as you like. The prices and nutrition information are not listed though. The most common orders are 3×3’s (read as “three by three”) and 4 by 4’s (read as “four by four”) that contain three and four layers of beef and cheese, respectively. However some people have ordered 20×20’s (pictured above) and even a 100×100!
RESPOND: Using the information from the menu, how could you calculate the cost of a 100×100 burger? Start your response with what you believe to be the cost and share a step by step explanation, in words and symbols, of how you worked it out.
Make sure your explanation is clear enough for a grade 5 student.
COMMENT: Find somebody with a different price and see if you can work out where they are going wrong in their calculation. (Or maybe they are right and you need to rethink, in which case, give them a “Like”) Check their explanation for clarity and see if you can offer suggestions where you think they have left gaps in their method.
The quality of student discussion and the depth of peer feedback was amazing! On sharing their ideas, each student had access to multiple strategies and, by working through one another’s solutions; they were quick to spot gaps in explanations. Similarly, some students realized that they had not broken down the problem correctly. Some had added additional buns, whilst others had allowed for too many cheese slices. By grouping the answers in Verso, common mistakes such as these, became increasingly visible and the anonymity supported low risk peer discussion of what was going wrong.
Following this lesson I used the same activity in another school but this time, followed up with Robert’s additional challenge, asking students to use a similar strategy to calculate the calorific value of the heart-attack inducing 100×100 burger. The powerful combination of using Robert’s organizational chart for planning responses and Verso to socialize ideas was a success, with students learning from their errors in the first activity and developing much clearer explanations. They were then tasked to create a formula to calculate the calorific value of all secret burger combos and an at-a-glance info-graphic allowing In and Out customers to make informed choices before selecting any burger combination up to and including the 100 x 100
If Robert Kaplinski can get me this excited about Math, then there is hope for everybody.