My last series of posts centered on standards-based assessment, which for several years has been the focus of much of my work with teachers. I’ve been somewhat dragged into this work. I think–a lot–about my experiences in my own classroom and the changes that I would make if I was to return. Assessment would come way down that list. It’s not that I had assessment figured out–I didn’t–but that shifts in other practices would take precedence. Throughout my SBA series, I addressed the same content learning standard: systems of linear equations. This got me thinking about one particular pedagogical do-over that I’d like to have.

A “concept-based” (and “competency-driven”) curriculum would highlight that solving a system requires finding an ordered pair (or set of ordered pairs) that satisfies both equations. In my classroom, I *talked about* this idea: “There are infinitely many pairs of numbers that make the first equation true. Also, there are infinitely many pairs that make the second equation true. But, there is only one pair that makes both equations true!” My students *listened to* this essential understanding; they didn’t *experience* it. Students as spectators.

A few years ago, the PAC at my kids’ school organized a plant sale fundraiser in time for Mother’s Day. Hanging baskets at one price, patio vegetables at another.

Simply translating this scenario into a word problem (like this one) doesn’t lead to students experiencing the big idea. Our actions, not posters, must communicate that “Learning takes patience and time.” A more patient problem-solving experience…

Give students *time* to play with possibilities: “What is a large/small amount that the PAC could make? What amounts could they *not* make?” etc.

Slowly reveal information. Remove one sticky note. How many of each did they sell?

Students will come to see, either within small–and visibly random–groups or through whole-class crowdsourcing, that there are many possibilities.

Remove another sticky note to reveal more information.

Students will observe that the eight (whole number) possibilities have become one. That is, they’ll experience the big idea about systems for themselves.

Remove a third sticky note. Ask “How *confident* are you?” This creates a need for students to check their work beyond catching incorrect calculations.

Remove the last sticky note.

In my Systems of Linear Equations videos from Surrey School’s video series for parents, I chose to apply this approach to a non-contextual naked-number problem.

Because of this choice, I might decide to use the plant sale scenario as an assessment item.

Tell students that the PAC has made the claim above. Ask “Do you agree? Why or why not? Convince the PAC.”

Admittedly, I haven’t added much to Dan Meyer’s systems of equations makeover from more than five years ago. (Man, I miss math ed blogs!) These ideas about *teaching* still interest me much more than “Is this Developing or Proficient?” For more patient problem solving see:

- Dan Meyer’s The Three Acts of a Mathematical Story blog post
- Brian Bushart’s Numberless Word Problems blog post
- Jenna Laib’s Slow Reveal Graphs site
- my What’s Going On in This Graph? blog post