What did SMP #1 say to the flash card? ……“You suck!”
We’ve been using a math reasoning inventory as our benchmark assessment for the past 5 years. In that time there’s been tremendous growth (in small pockets), but unfortunately our struggles continue. This post was inspired by Robert Kaplinsky‘s How Old is the Shepherd?
I’ve been videotaping some of our final benchmark assessments so I can use them in a future PL (if accepted…NCTM 2015). I thought I was going to capture “all the great things happening” and that these recordings would inspire teachers. This video IS NOT what I intended to capture but fortunately it may have a greater impact.
He sounded so convinced and confident in his answer. I asked some questions that would hopefully get him to reason abstractly and quantitatively but to no prevail. “9!” This student has been labelled as “good at math”. So I grabbed some index cards…30 seconds later:
I knew it!!!! It’s suddenly became apparent that MY definition of “good at math” is all screwed up. If flash cards determine a student’s mathematical ability then I haven’t assessed my students in years (and proud of it!).
Maybe flash cards should be banned from schools and considered as contraband. Maybe we (teachers) should have to come to school with clear plastic bags and see through roll-away crates to ensure that Weapons of Math Distraction are not being snuck into our schools. Maybe Weapons of Math Distraction: Nonsensical Tools used in the Math Classroom could be the sequel to the book Nix the Tricks.
Maybe one teacher will change when they see this video…maybe!
Fascinating post, Graham. Hope you don’t mind, but here are some questions/comments.
1. How do you use the math reasoning inventory?
2. The student clearly knows his basic division facts. Is building this kind of fact fluency a regular part of your program? If so, what do you do?
3. I’ve listened to his reasoning several times and I still want to know how he came up with 9 as an answer. This would be great on Michael Pershan’s Math Mistakes site. I love this kid and want him to be right! The way he just pushes those counters out of his way! He does generate the number 5, but then adds 4. So where did he get that 4? Is it possible that there was something about the picture of the tables and the chairs that confounded his understanding? There are 4 chairs lined up after that first table in the picture.
Thanks. You’ve inspired me to try to capture some of this kind of activity with our students here.
Hey Joe…THIS THING IS A BEAST!!!!
1. We use the math reasoning inventory as a “silver bullet”…if there is such a thing in education. In a nutshell we use it as a benchmark (3 times a year), common assessment across the county, and as a universal screener for RTI. And because it addresses all of the above it serves as a diagnostic, formative and summative assessment.
2. Building fact fluency not an explicit part of the Numeracy Project but many teachers at our school and district have focused on strategically developing fluency in their students through Number Talks and in the order that John Van de Walle suggests. Both of these resources have helped students conceptually develop fact fluency. The automaticity of facts is built through games and purposeful practice. We’ve really tried to shy away from timed tests because of their negative effects.
3. You nailed it! This kid was oozing with confidence and I talked to him the next day to better understand what he was thinking. He got the 5 because of the one-fifth and he said 4 because of the table’s 4 sides. What I really like about this question is that students have to truly make sense of the problem AND not rely on the picture to solve it (SMP1). Some teachers think it is unfair because the picture tricks students. Not sure I agree though.
I’ve been tinkering with a Reasoning Inventory post for some time and now I probably just need to finish it up…thanks for the push. I’ll share whatever I have and I’m only an email away if you dive in. I look forward to watching some of the interviews you post on your blog!
All the best,
Graham
There is a definite disconnect between the number and it’s value. It was interesting to see him push away the counters in the first video, and to listen to his math reasoning. He subtracted the five to get 20… Then he added the four to the five to get nine. He obviously had a math understanding he was acting upon. I think these videos will make great teaching tools, at many levels!
Absolutely Cleargrace!
I think showing these 2 videos (one after another) will lead into some great conversations between teachers. It appears as if he knows his facts but is unaware how to apply them to a context. All the more reason conceptual/contextual teaching supersedes procedural/memorization.
I’ll definitely be sharing a future post about the conversations teachers have after I share these videos.
Keep spreading the GloSS and IKAN love! Inoculate the world against surface understanding. I think your understanding of good at math is spot on. This kiddo will get there, thanks to your refusal to assess in a shallow manner.
Thanks for the introduction to this wicked goodness 99! If not for you and 86 I’d probably have no idea how to diagnose or when to medicate!
Cheers and thanks for helping me Get Smart!