Focus on Math

Helping children become mathematicians!

Is the Task Worth the Time? September 18, 2015

Filed under: General Math — Focus on Math @ 4:42 pm
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blog picAll the learning minutes of the school day matter — in fact, if you are like me, often what I had planned for a given school day was not accomplished. Things took more time than I had expected, or there were interruptions to the day. The learning time seemed to go by so quickly.

Because learning time is a precious commodity, it is critical that we, as educators, think carefully about what mathematical tasks we are giving our students to do. Is the task worth the time it takes to do it? Are we getting good value for the time spent? Are we getting “bang for our buck”?

This is true for teachers at every grade level. But I am going to be a little bold here and say this is especially true for primary teachers: those who are teaching students in Kindergarten, grade 1, grade 2, and grade 3. There are so many activities available at the touch of a computer key, but certainly not all of them give us good value for the time spent.

Two examples of such activities are pictured here. In one, the students are asked to colour the picture based on the sums of the problems on the page. Can you see the problem with this task? The students are likely to spend more time colouring than engaged in math thinking. There is nothing wrong with colouring — I know it helps develop fine motor skills in these little people. The problem is that much of the time set aside for math is usurped by the colouring part of the activity. In the second picture there is a similar conflict. There are five math questions to solve, but the cutting and pasting of the numbers for the answers will take much longer. Again, cutting is a great skill, one which students should develop. I just think it is sad to have students cutting and pasting during math time in which I can have them developing number sense through more meaningful tasks.

I want to encourage you to jealously guard the math learning time that you have with your students. Use your critical thinking skills to evaluate prospective tasks (no matter where they come from!) and choose those that are truly valuable, those that don’t waste math time. By all means, have your students cut, colour, and paste. Just do it in art time, not math time!

According to Howden, number sense “develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Arithmetic Teacher, NCTM, February, 1989, p. 11.) Is your activity one that allows students to explore numbers, visualize them, and make connections to other math concepts? Is the task worth the time?

Mathematically yours,

Carollee

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A Small Change but a Big Result May 13, 2011

Yesterday a teacher in our district, Kevin, shared with me a wonderful story about math in his classroom. Kevin and I go back a ways — I was the Faculty Associate when he completed his Professional Development Program (student teaching) through SFU, and he had also taken the “how to teach math” course from me. He was hired in my district, and he has spent most of his career teaching at a rural K-12 school where for the past number of years he has taught the gr 8-12 math courses.

Kevin told me of his frustration, as well as his students’ frustration, in the math classes over the last years. He would present a lesson, have the students begin working on the problem set in the text book, and then have the students do the remainder of the assigned problems for homework. However, invariably the students had difficulty with the homework problems and would become increasingly frustrated with trying to solve those problems. The next day Kevin often felt he needed to get on with the new lesson, but clearly time was needed with these homework questions which, being later in the practice group, were often the more difficult problems in the set.

Kevin remembered the emphasis I had put in the “how-to-teach-math class” on the power of students solving problems, and he decided to change up the class time with his students to see if he could incorporate more problem solving in his class.  So, instead of this:

  • teach a concept
  • do the first, easier problems in the practice set in class, students working together
  • send home the later, harder problems in the practice set, students working alone,

Kevin changed his time with students to look like this:

  • do the later, harder problems from yesterday’s lesson in class, students working together
  • teach a new concept
  • send home the first, easier problems as homework, students working alone.

Kevin found this to make a profound difference for his students. Where many of them had felt unsuccessful in math, never being able to complete the homework on their own, they were now able to do so. This began to build their confidence. When they worked on  the harder problems together in school, most students found the knew most of what to do. Sometimes they were forgetting only a small step. Kevin realized when the students had tried the problems at home, if they could not arrive at the answer at the back of the text, most would erase all of their work, believing they were completely off track. Working together in class students had the opportunity to make connections to previous lessons, to communicate their thinking, to reason about the logic of what they were doing, to justify their answers. By engaging in these processes day after day, the students began to build a set of problems solving skills and strategies than empowered their mathematics thinking.

The three “chunks” of the lesson really did not change, but in changing the order in which they happened (which in turn changed which problems were addressed through the mathematical processes**) Kevin facilitated a change in student understanding and success. Way to go, Kevin!

I hope you will look at how math is going in your classroom and see if you need to turn it “upside down”!
Mathematically yours,
Carollee

P.S. The NCTM lists the process standards as these: connections, communication, problem solving, reasoning and proof, and representation. More information about these can be found at this link:
http://www.nctm.org/standards/content.aspx?id=322
In BC, and for the members of the WNCP in Canada, the mathematical processes are defined as these: communication, connections, mental math and estimation, problem solving, reasoning, technology, and visualization. More information about these can be found in the “front matter” of the BC IRP curricular documents found at this link:
http://www.bced.gov.bc.ca/irp/subject.php?lang=en&subject=Mathematics