There’s been lots of discussion in the news lately about teaching math in Ontario. The falling EQAO scores in math have resulted in more support for teachers, and I do think that professional development to improve practice is a good thing. Right now, as a Grade 5 teacher in the Hamilton-Wentworth District School Board, I’m involved in professional development sessions on proportional reasoning.
How Many Nickels Make a Dollar? from EQAO on Vimeo.
Tomorrow afternoon, I’m meeting with other Grade 5 teachers from my school and a neighbouring school to discuss an assessment task that we did on this topic as it relates to fractions. Yesterday, I blogged more about how I was going to approach this assessment task, and I was very excited to see how things went.
Students were definitely engaged in the fraction centres this morning. There were lots of interesting discussions at each of the tables, and students were looking at different ways to create different fractions. Talking to the students throughout the process, I got a good glimpse at what they understood and what they did not understand when it came to fractions.
But then it was time for the assessment, and overall, students were not transferring their skills. Why? I think it’s because rote learning is not enough. It’s funny: I was actually talking to a parent about this topic yesterday afternoon. She was discussing our approach to inquiry in the classroom, and her concern was with inquiry in math. How do students get the skills that they need? I said that I’m not against students learning certain specific skills (e.g., memorizing their multiplication tables), but I think that they need to understand these skills in context. Project-based learning and the inquiry process gives meaningful context to these skills. It helps students not just learn what to do, but understand why they do it. This “thinking component” helps builds deeper understanding.
For many of my students, they knew the basic concepts. They understood that splitting a circle into four and shading in one is 1/4. They understood that you can divide an object into two equal pieces, and that’s a half. They also understood the concept of “fair sharing,” and the importance of dividing pieces equally. All memorized facts, they knew, but the thinking piece was missing. When students had to share two fractions that were close to 1, with one fraction being slightly closer than another, they struggled with how to compare fractions. Many students chose fractions with unlike denominators, and then they didn’t know how the two equated. A large number of students saw bigger numbers in the numerator and assumed those were the bigger fractions, but they didn’t look at the proportions, including those highlighted in the pictures that they drew (e.g., they would say that 2/6 is closer to 1 than 1/2 because 2 is bigger than 1). A large number of students also didn’t realize that 1/2, 1/3, 2/5, and 10/11 are actually all smaller than one. While they could read all of these fractions, they didn’t really understand what they mean, which resulted in a limited understanding of how they compare to each other.
I know now that Jonathan So’s approach to fractions is going to be essential. I also know that I’m going to need to give the students more real life contexts when it comes to fractions, and give them lots of opportunities to compare fractions. They need to move beyond their memorized facts to a true understanding of what fractions mean. This fractions activity actually taught me a lot about approaching all math topics: it is a balancing act between knowing the facts and understanding the concepts. Memorized skills can be great (in some cases), but students need to be able to think as well. That’s where meaningful math problems, matter.
What do you think? How do you approach this “balancing act?” I’d love to know your thoughts.
Aviva
Great reflection. Balance is the key but even moreso conceptual before memorization. I am not saying that students do not need there facts BUT without understanding there is no growth. I have had this debate for eons (or at least it feels that way), but I stick to my guns and teach concepts. Why? Because I know that through good contextual problem solving kids will develop factual knowledge and I also do it on the side through games.
I had a debate a little while ago on this topic and I asked, ” did you become a successful businessman from memorizing procedures and ways of doing things?” I didn’t get an answer but I think the answer was no. So if that was the case why should we expect rote the be the only answer or because of the lack of it we are failing.
Your right kids need balance but they need conceptual, concrete way before prie memorization. Once they have the concrete then memorizing becomes easy. I have students who compare fractions without converting the denominator because they know that as the denominator gets smaller the piece gets bigger. They have that understanding so it’s easy to say that 4/5 is larger then 3/4 because 1/5 is smaller then 1/4 and therefore closer to a whole.
As for how I balance, mostly through games. We have a game Friday and every strand has five or so games that go with the problems. They build recall and they teach understanding. We also do a fact recall every Monday and strings or mini-lessons really help set the mental component and dialogue. Keep at the concrete developmental learning, all will follow.
Jonathan, I had my aha moment reading your comment. What you say about conceptual knowledge before memorization makes so much sense to me. I think that the problem is that many of my students have the opposite. In the case of fractions, they’ve learned the memorized facts but with limited to no conceptual knowledge. We need to work on this important missing piece.
Just a couple of questions about your approach:
1) How do you link these games to a real life understanding of the problem? After a game experience earlier this year, I’m very aware of the need for the students to understand the “why” behind what they’re doing. Maybe the other meaningful problem solving activities help with this in this case. I’m just curious.
2) What do your fact recall Mondays look like? What do you do for the students that already know their facts?
Thanks for the help, Jonathan! I’m seeing some more “changes” in my future, and I think these could really benefit my students. 🙂
Aviva
P.S. I think your ideas may be making their way into our meeting this afternoon. 🙂
Math games aren’t really connected to the context, as much as they promote fun ( and learning). The real purpose of the games is to learn facts and recall them faster. My students play them with their math partners, after they finish their math problem and on Friday. On Fridays we have discussions about strategies that they used, how they won and what improvements they are seeing. We also sometimes, talk about how they use these strategies in problems, does it help? Things like that. You could connect them to contexts but they are more for the fact part, without the strict memorize no talk part. I find games allow you to balance that part. Students get to practise facts and students also talk about the games and strategies they used. I also have ability partners so that way one person isn’t dominating and doing all the work.
Fact Monday looks like the old mad minutes but the difference is students pretty much get twenty minutes to answer as many questions as possible. This does not work with every community. My community loves to challenge themselves around knowing facts. I also tell the kids it’s not how much you answer but that you are improving from month to month. We graph our results and write reflections on what needs to be done to get better. This helps the kids who do well and the ones that don’t. For the kids who get it, I add the element of time, but only when they are ready, everyone else is based on getting their facts to be recalled.
Hope that helps. I am always available to talk via twitter. Keep me posted on your pd. Love math!
Thanks Jonathan! I really appreciate the further explanation. The “talk part” of the math games I think are so important, and I like how you sometimes try to bring it back to the learning through the math problems (even if that’s not the original intention of these games).
Thanks for also sharing your Fact Mondays. I love your differentiated approach: only adding in the time element when the students are ready. The reflection piece is wonderful too. What a great way for students to be aware of what they need to do to get better.
You’ve given me lots to think about here! I’m sure I’ll be sharing at least part of our discussion at my Math PD this afternoon.
Aviva
‘A Balancing Act’. Great title.
The best thing that made it easy for me in my EQAO days were little ‘popcorns’ our teacher would bring in. Everyday after second period we would usually have math, and the teacher would bring in a batch of freshly made butter popcorn.
We used that popcorn not only for eating, but also as a muniplative. And just before home time she would hand out a quiz about the preffered unit. The marks you get=Popcorn you get.
For me it wasn’t a big deal. But see how students were urged and fascinated into the math and learning world. Use stratergies (even if it includes extra cleaning up the floor 😛 ).
I don’t think you should take it too hard. Students have not learned the concept, and it was just a quick early hand assesment. Another thing is something called: Test Thursday. Small games such as Around The World (multiplacation) are good for the mind. Encourage your students to try even if they are near the smartest person in the class. This will balance the learning and assesments so students will be ready for anything like this.
Glad to hear your day worked out!
P.S. I have met a new person on the Commons! It is a student of yours, Katerina. We’ve become great online pals! She is very bright and nice!
Yusra
Thanks for sharing your ideas, Yusra! There are definitely lots of different approaches, and I think that balancing the memorized facts and application questions are important. I really believe that students need to know more than just WHAT to do, but WHY to do it. The popcorn idea is an interesting one, but how did the students feel if they struggled in math? How was everyone successful? I’m always thinking about this.
It’s always great to hear a student perspective, and as usual, I really appreciate you chiming in!
Miss Dunsiger
P.S. I saw that you and Katerina are communicating through The Commons. What a great connection for both of you!
Well, it was not exactly an assement in the unit for the popcorn unit. So if they struggled they would leave the question out. The teacher recorded the results for future goals and references.
Everyone was succesful because the teacher told us that the best thing was that we tried.
Hope that helps!
Yusra
Thanks Yusra! This does help. I appreciate you explaining more.
Miss Dunsiger
No problem! Thanks! I will await your next post! *tapping foot… tapping hands on table…. pulling out my hair….* 🙂 Just joking take your time! 😛
Thanks Yusra! Glad you enjoy my blog posts so much. I always appreciate your student voice!
Miss Dunsiger
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