positive and negative numbers Archives - Mathematics for Teaching

One popular way of introducing the negative numbers is through the number line. Most textbooks start with the whole number on the number line and then show to the students that the number is decreasing by 1. From there, the negative numbers are introduced. This seems to be something easy for students to understand but I found out that even if students already know about the existence of negative numbers having used them to represent situations like 3 degrees below zero as -3, they would not think of -1 as the next number at the left of zero when it is presented in the number line. They would suggest another negative number and some will even suggest the number 1, then 2, then so on, thinking that maybe the numbers are mirror images.

Here is an alternative activity that I found effective in introducing the number line and the existence of negative numbers. The purpose of the activity is to introduce the number line, provide students another context where negative numbers can be produced (the first is in the activity on Sorting Situations and the second is in the task Sorting Number Expressions), and get them to reason and make connections. The task looks simple but for students who have not been taught integers or the number line the task was a problem solving activity.

sorting expressions — Question: Arrange from lowest to highest value

When I asked the class to show their answers on the board, two arrangements were presented. Half of the class presented the first solution and the other half of the students, the second solution. Continue reading “Teaching negative numbers via the numberline with a twist” →

I’m working with a group of Year 7 mathematics teachers doing Lesson Study for the first time. The teachers chose to do a lesson study for what they believe to be the most difficult topic in this year level – integers. Part of my preparation as facilitator is to draw a map of what I know about teaching the topic. The map is more than a concept map because it includes not just related big ideas or concepts but also how these are taught and learned. Hence, I call this pedagogical content knowledge map (PCK map).

The PCK map I present here is a product of my own readings and my own experiences of teaching the topic. This means that it may not be the same as other teachers especially the ‘teaching part’ of the map, the ones in orange colors. For example, experience and research results back my claim that the number line is a very good way of representing the set of integers but not in teaching operations. Click here for my post about this. Notice that I gave emphasis on students knowing when a negative, a positive or a zero result rather than the rules for operation. I believe that without this, a conceptual understanding of the operation involving integers will be weak. Also, experience has taught me that although integers are numbers, the teaching of it must be algebraic. The instructions should be so designed so that students are learning algebraic thinking as well. I have noted this in the PCK map.

The map is not yet complete. I intend to include descriptions of effective activities and students’ learning trajectory of the concept after my research with the teachers. Please feel free to give your comments and share experiences for teaching integers that I could look into in my study.