Writing in Mathematics

Teaching students to communicate mathematically is essential if you wish to raise any standardized test scores. The last few years I have tried to include more justify your response questions into my classroom. Why? When a student can communicate their mathematical ideas clearly many positive things occur - it deepens the meaning of the concepts they are learning, it helps students retain information, and it strengthens their use of proper mathematical vocabulary and proper notation. Of course, students struggle with writing their mathematical explanations. It is important that the classroom teacher not give up on this endeavor. To help the students, model the written communication on a regular basis. I have found studying and analyzing responses to released state test questions and released AP questions have assisted me and my students greatly.

Reading in Mathematics

The opening of another school year is coming fast! Time to contemplate various goals. What area or areas do I want to focus on? Our students take so many important standardized tests, how can I help them be more successful? I believe if our math students did a better job of reading the test questions, they would have a greater chance of answering the question correctly. Many times I hear students say they just didn't understand what the question was asking.

Consequently, we need to help our students develop solid reading skills within the context of mathematics. Active reading strategies of underlining text and circling key words help, but is there more we can do? I recently came across a K-N-W-S strategy / template. Tom Stull, a high school math teacher from Ludlow High School, has developed this guide. Students use the guide to assist them when analyzing word problems.

K - What facts students KNOW
N - What information is NOT NEEDED
W - WHAT the problem is asking them to find
S - What STRATEGY they will use

Tom has quite a few reading strategies that he shares which can be found on the More Reading Strategies in Action - Mathematics High School. For those of you interested in other levels or other areas, the More Reading Strategies in Action website has some great resources available.

The Last of the Complex Diagrams

If you tried the previous problems for the past two posts, I have two more for you. I use both of these problems at some point in time in my classes. They are both excellent for stressing the importance of organizing thoughts and work. I also ask my students for a written explanation of their problem solving strategy.



The triangle question really forces one to be very organized in order to find all 28 triangles. This is a great problem to have students work together on.



The square problem allows one to analyze a pattern. When discussing this problem have students make up a list of the number of individual squares, of squares made up of four smaller squares, of squares made up of nine smaller squares, etc. The students should see a pattern occurring. This will allow you to move into examining patterns and finding rules.

Killing many birds with one stone

If you started to create the "thinking" environment with the previous rectangle problem (by the way there are a total of 9 rectangles), then you want to continue along this line. I would suggest that the next day you have a second problem similar to the previous one for students to work on. I have created a triangle problem.



This problem allows me to accomplish several goals. First, I give it to the students as soon as class begins. This allows me a chance to take care of administrative details like attendance. Second, after they have worked on it for a few minutes, I ask them to check with their neighbor to see if they agree. If they don't agree I ask them to try to decide which answer is correct. This problem is more challenging than the previous, so usually students do not agree on the answer. Consequently, I have them discussing their methods and they are engaged. I will ask them what they think the answer is and I will write these answers on the board. Now, I have the opportunity to accomplish my third goal which is to stress the importance of organizing their thoughts and their work. I will number the individual triangles and then I will make a list of triangles I am combining to form another triangle. After we discuss various strategies and discuss methods of organizing their count, the students usually beg me for another one to try. I tell them we will do another one tomorrow and there will be prizes for those who get it correct. Consequently, I have them looking forward to coming to math class! So, this quick activity from the day before which had the purpose of creating a safe thinking environment has provided me many benefits including the engagement of my students in problem solving!