MVP 4.1 Debrief and Next Steps

Last week, I wrote about my plans to teach lesson 4.1 in the MVP curriculum introducing solving equations.

There were definitely both highs and lows.

First, the highs:

The 3 reads strategy went super well! My gen-ed kids were SO not into the reading out loud in unison thing, so they did their reads in partners. I found it was better to tell them to read in the story in partners for two minutes and THEN give them the prompt to answer, rather than giving them the prompt at the same time as telling them to read.

The sheltered ELL students, however, LOVED reading in unison, and gave themselves a round of applause after finishing each read-through. Most importantly, they made sense of the context in a genuine and authentic way.

 

This next one might count as both a high and a low. The following statement uses a form of the verb “to leave” both to mean “go away” and to mean “stay”:

Screen Shot 2018-03-04 at 7.20.15 PM
 The students at the front table separated into three equal-sized groups and then two groups left, leaving only one-third of the students at the table. 


I’m not joking when I say we spent a solid 15-20 minutes discussing this in the sheltered classes. That being said, they did understand it, and felt quite proud of themselves for getting the nuance. I apologized for English being such a tricky language, and one of my students muttered to himself, “Change the English.” If only I could…

Now, the lows:

The teacher notes for this lesson begin with this sentence: “In this task students will develop insights into how to extend the process of solving equations—which they have previously examined for one- or two-step equations—so that the process works with multistep equations.”

But here’s the thing, most of my students have not previously examined the process of solving one- or two-step equations.

I knew this going into the lesson, but I also wondered just how much of an impediment it would be. The lesson is designed around building an intuitive and conceptual foundation for solving equations, so maybe we could skip over one- and two-step and just hit the ground running with these multi-step equations.

The work that I saw last week has convinced me that that is not the case. My students REALLY struggled with the notion of “undoing” operations and working backwards to find a solution.

Side note: the first order that the Post-It Notes are presented in has a fundamental flaw – you can arrive at the correct answer with incorrect reasoning!

Screen Shot 2018-03-04 at 7.29.53 PM
·      Some students are sitting at the front table. (I got distracted by an incident in the back of the lunchroom, and forgot to record how many students.)
·      Each of the students at the front table has been joined by a friend, doubling the number of students at the table. 

·      Four more students have just taken seats with the students at the front table.
·      The students at the front table separated into three equal-sized groups and then two groups left, leaving only one-third of the students at the table. 

·      As the lunch period ends, there are 12 students seated at the front table.

Specifically, the process should be:

12 * 3 = 36

36–4 = 32

32/2 = 16

But students can completely neglect inverse operations and do the following:

12/3 = 4

4+4 = 8

8*2 = 16

So, in the future, I plan to change the order of the Post-It notes so that that doesn’t happen!

Not only did my students struggle with conceptualizing the need for inverse operations (and I think the multi-step nature of the problem contributed to this), they also seemed to have no prior intuition for the notion of keeping an equation balanced.

Only a couple of my classes got to the point where they were trying to solve the equations at the end of the lesson, and I mostly saw guess-and-check and some working backwards with informal notation.

Future lessons in this module need students to be able to solve equations with the traditional, formalized notation, but I’m still working on building students’ intuition and conceptual understanding.

As a result, I’m going to take a quick break from MVP and do a couple of lessons from the Illustrative Mathematics 7th grade curriculum.

Specifically, lessons 6.7 and 6.8, which use the notion of balanced hangers to develop both the intuition and the notation for solving equations.

I think that next year, I would probably want to do these lessons before MVP 4.1, rather than after it.

 

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