Our grade 9 academic math course begins with polynomials and exponent laws. Ugh. Students struggle with this unit above all others and it is what we hit them with first. I had thought of changing the order but since taking Jo Boaler's "How to Learn Math" course, I think the problem lies in HOW we are teaching it. We need to work with patterns instead of having students simplify abstract expressions by remembering (or not) rules. What worked for many of us, does not work for so many of them. Attempting to work this in while keeping peace with my co-workers is challenging. We all teach the same thing on the same day using the same lesson. This can be a fantastic model if teachers are on the same page and truly working collaboratively...
I started by creating an activity sheet for kids to work through five linear patterns involving only positive quantities and five linear patterns that use positive and negative objects.
I stole most of these from Fawn Nguyen's Visual Patterns site. Thanks to Fawn's brilliant post on Pattern Posters for Algebra I, I have a better framework for what I am doing. I will start by working through a pattern with them (this is straight from Fawn - have I mentioned how much I love her?).
Or maybe two. You see, I am still not sure what I'm doing. By that I mean that not having done this particular activity in this course before, I'm not sure how it will play out. What patterns they will find. Whether they will differ from each other's and mine. What I will need to ask to get kids to persevere or get on the right track. How long it will take. I am fine with not knowing how it will go - I know where I want them to get and have a good idea of how to help them get there. However, I find it very difficult to just give this "lesson" to other teachers who may or may not buy in. I feel like I need some kind of narrative to go with it, but I don't have my own yet. Add to that the fact that the time will have to be "shared" with review from grade 8 (order of operations, working with fractions and integers) makes me feel overwhelmed. I would like to take the time to do this properly and I believe in doing that, the review will happen naturally. But I know that will not fly with some of my colleagues so I have to try to make it all work together. And I need to have this sorted out by tomorrow (!) as others need to photocopy. So any advice you can give would be great!
I am in the same place as you - getting 4 of my own kids ready for school, starting with students a week from tomorrow, so many great ideas from twitter, blogs, and #howtoteachmath and just that - how do we get buy in from other teachers if they haven't spent their summer doing the same thing as us. If I was your colleague, we would be all set!
ReplyDeleteYes, the MTBoS is so fantastic and so overwhelming with great ideas! It is hard to understand it without being part of it.
ReplyDeleteMary - I really feel your perspective here.
ReplyDeleteI agree that connecting algebra to patterning using visualization is key.
In terms of getting everyone on board, maybe starting with a couple of key lessons / activities (like the one you're developing) then growing from there? There is a lot of research, practical experience and resources behind the approach you want to take. I also agree that integrating review of key ideas and building connections naturally through new content can be more effective (and efficient) than doing all of the review up front - maybe a compromise is to do a quick basic review up front (like BEDMAS, fraction operations) and integrate the rest as you go?
If I was your colleague, and unsure about your approach (because I hadn't been plugged in to the MTBoS) I think I'd WANT you to try it out, and keep me in the loop - maybe even let me observe a lesson or two - so I would feel more confident myself trying it next semester. Might this be an approach? Could you carve yourself a little leeway to "pilot" a few lessons?
By the way - here's a newly released publication from the Ministry that may help with your narrative: Paying Attention to Algebraic Reasoning. http://www.edu.gov.on.ca/eng/literacynumeracy/PayingAttentiontoAlgebra.pdf
Mary,
ReplyDeleteHere is CT's first unit on patterns - linear and exponential. http://db.tt/k8JtePdm If you like any of it, go to atomicmath.org, and you'll find a link to instructions on how to access the entire black-line master curriculum, without assessments. Then you can download, edit, etc.
I also tried to do an area model thing for exponent rules, but it isn't great. http://www.geogebratube.org/student/m41965?mobile=true
Good luck!
No, I don't think you can ever mention how much you love Fawn enough. She's quite insecure and needs heavy doses of love or she'll wither and die. Pitiful really.
ReplyDeleteOver the years I've gathered enough activities to choose from for first day activities, yet I keep going back to using the "Patterns Poster" as my first one because it just works for me and my kids. (And whatever else I've already mentioned on the post about it.)
So today was our first day, and we worked through one pattern (Pattern #2) as a class, and everything went as well as I could hope for. Kids are now working on their one randomly given pattern (1 of the 20 that I'd shared on Twitter). Lots of good questions, the big one to start with was what is considered a "unit" that they need to look at that's changing: the entire hexagon as a unit or each side/toothpick that makes up the hexagon. Already one student has written an equation that is quite different (doesn't match) from his verbal description of what step 13 might look like, so we should have a good conversation from this tomorrow. Another common error is kids not writing expressions in parentheses as a quantity, so this allows me to talk about how they see each "group" of objects, and each group is a quantity by itself.
We really never know for sure how things turn out until we actually do it, Mary. It's worth the risk, and something we want kids to do too.
I really like your cupcakes and ants integers pattern!!
You know I love you like crazy, Mary. Everything will be okay. Your colleagues can only buy into something that you wholeheartedly do so yourself. And when they don't, who needs them anyway?? :)
Love the ants and cupcakes! I use sharks and surfers, both very poorly drawn by me. :-)
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