“…some seemingly simple ideas are not always as simple for students as they seem to adults.” -Lesley Booth How often have you seen students make the following type of mistake? 2a +5b=7ab My guess is that if you teach algebra, you’ve seen this mistake more than once. If we believe that students do things that …
In a 1982 study by John Clement, 150 freshman engineering students were given the following problem: Write an equation using the variables S and P to represent the following statement: “There are six times as many students as professors at this university.” Use S for the number of students and P for the number of …
Let’s say you have a binder full of the data I talked about last time. You know which students got which questions wrong on your latest assessment. How do you use this information to help those struggling students? You can’t. Knowing they answered a question incorrectly is useful, but you need to know why. That’s …
How to gather the data you really want about student misconceptions Read More »
During school visits, I rarely make it five minutes without hearing about “the data.” I am shown big binders containing spreadsheets of data. I sit in data meetings where teachers furiously highlight lines in spreadsheets and calculate percentages. Principals tell me how data are being used to evaluate students and teachers. Some of this is …
In my last post, I suggested a way to build on what students already know to introduce the equal sign. Let’s say you followed that plan and your students are now proficient in using symbols to describe a quantity as equal to, greater than or less than another quantity. What do you do next? Use …
I’m certainly not the first person to talk about the importance of the equal sign. Researchers have been talking about it since the 80’s and discussions about the equal sign have made the rounds on the blogs and twitter (most recently Justin Aion posted about strings of equal signs here) Often, the concept of equality …
Equality: How elementary school teachers can help algebra teachers Read More »
Although I loved the first day of school, September was always a difficult month for me as a teacher. It’s a month of establishing classroom norms–the rules and expectations of your classroom. What it means to have a conversation about math in your class may be different than what it means in another class. As …
I love the first day of school. I love sharp new pencils and blank notebooks. I love meeting new students that will change your life in ways you can’t even begin to imagine. Most of all, I love the hope it presents. It’s a chance to do things differently. Many of you are excited to …
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 »