This year was the first time I’ve presented at the NCTM annual meeting. In one session, I talked about my work on helping students build justification with fractions. In the other, I presented with Megan Gundogdu about how we have been using lesson study to build capacity at a middle school in the Bronx. I really …
I’m planning a PD for a group of elementary math teachers that I’ve never met before. This makes things difficult because I don’t know anything about what they know or what their experiences are. I was told that one of the sessions should be about engaging students in doing mathematics–which is what I think all …
One of the things that is particularly interesting to me right now is how we help young students develop the ability to justify why things work in math. Often, kids know the correct rule but have no idea why the rule works. When I ask them to explain why a rule works, they wind up …
I’ve been spending a lot of time in schools and classrooms these past two weeks using diagrams with students and teachers. As a result, I’ve been neglecting this blog but I’ve been learning so much. Hopefully, I’ll start making more time to write about what I’m doing. Here’s the latest problem I’ve been tackling with …
Using Diagrams to Make Sense of Fraction Word Problems Read More »
Read the following problem and think about how a student might solve it. There are 250 students in the fifth grade. Three-fifths of them speak two languages. How many speak two languages? As I’ve mentioned before, I’ve been introducing tape diagrams, or bar models, to students and teachers recently as a way to solve word …
Recently, I’ve been investigating Realistic Math Education (RME). I like the idea of building on what is real to the student. Because I spend a lot of time thinking about fractions, I wanted to know how RME approaches them. Luckily, Streefland wrote about his three-year teaching experiment in the Netherlands. In the experiment, students were introduced to the “Fractured …
One of the most important things you can do when you introduce fractions is to let students break things. Give them lots and lots of experiences where they have to break up things evenly and share things fairly. For example: Have them fairly share 3 cookies with 2 friends. Have them fairly share 5 granola …
Do the following tasks look familiar? What fraction of the circle is shaded? Shade in 2/3 of the rectangle below. Are most of your students successful at these types of tasks? I would be willing to bet that they are after trying a couple of them. However, I’d also guess that once you move on to …
Assessing what students really understand about fractions Read More »
One of the most common ways to introduce fractions to young students is to talk about ¾ as “3 out of 4.” And it’s part of the reason why students have so much trouble with fractions later on. Researchers Siebert and Gaskin (2006) wrote about why introducing fractions as “3 out of 4” instead of “three-fourths” …
5 reasons you should NOT talk about fractions as “out of” Read More »
The three representations above can all be used to model two-fifths. Does it matter which one you choose when introducing fractions? In my last post, I talked about why concrete objects or models can be helpful in building on what students can do. What I didn’t talk about was how to choose a model …
How do you choose what model to use when teaching fractions? Read More »