Since January, I have taken on another job as a math coach for a local school district. It has been very exciting. The teachers in this district have made me feel extremely welcome. I have copied below a series of email messages that were recently sent back and forth among a couple of special education teachers and myself. You will find my response to Jim’s question at the end of this series. My hope is that others will chime in with your thoughts, too, since middle school is not my area of greatest expertise. Here is the first message that started this conversation:
Hi Jim -
I didn’t know if this information would be of use for you, but here is one of the things the math coach at JWE has recently sent out. [Anna is referring to the weekly math notes I sent out to everyone. She forwarded it on to Jim as an attachment to this message.] I haven’t actually met her yet, but I know some of the teachers are excited about her as a resource.
Thanks,
Anna
Here is Jim’s response to Anna and I was cc’d as well.
Thanks, Anna.
This was interesting. My questions is more to do with math calculations and whether or not we should be putting significant time and resources into trying to get our older students (7th/8th) to learn the multistep strategies they have not been able to learn in their first 6 years of school. Should we be prioritizing our time this way if a student is able to accomplish accurate calculations with the fluent use of a calculator. I wonder at times if it is a wise choice of time and resources when we put math calculation goals on IEP’s for our older students who are being successful with calculations with their calculator.
Thanks for thinking of me.
Jim
Before posting the the blog, I checked in with Jim to let him know what I was thinking and asked his permission to use this question as a blog entry.
Jackie,
That sounds fine. Again, I want to clarify that I am talking about our older students who have not been able to learn the strategies in years of instruction. Obviously there are some brain function issues in play. If a student has missed a significant amount of instruction or is in 6th grade or lower, I think it is more appropriate to carry these goals on an IEP. I am meeting a ton of resistance from students trying to slow them down to learn these strategies they have not learned. Would our time be better spent by engaging students in a calculator curriculum gaining them functional skills that will allow them to independently complete regular class math curriculum?
Thanks for your help with this question.
Jim
And here is my response to Jim’s very thoughtful question.
As I mentioned in our previous correspondence, I think this is a very complex question. On the surface, I would agree with you that helping students utilize a powerful math tool like a calculator reaps a great harvest. I have collected many math calculator games and activities over the years because I see how vital it is for students to be able to use this tool fluently. On the other hand, I see students developing computational fluency through a multifaceted approach. As I shared in a previous blog entry, the following quote comes from Foundations for Success, the final Report of the National Math Panel.
“The mathematics curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. The development of these concepts and skills is intertwined, each supporting the other and reinforcing learning.
Teachers can help by providing students with sufficient practice distributed over time and including a conceptually rich and varied mix of problems to support their learning. In addition, teachers should encourage and support students in their efforts to master difficult mathematics content. Students who believe that effort, not just inherent talent, counts in learning mathematics can improve their performance.”
At the intermediate level and above, students need to be fluent in mental math, paper and pencil methods and using technology such as a calculator for computing answers to situations involving numbers (both whole numbers as well as fractions and decimals). Another often overlooked or underdeveloped aspect of computational fluency is not only being able to compute in all three of the ways mentioned above, but also knowing which method is best used based on the given task. In addition, students must be able to determine if an exact answer or a close approximation (estimate) is sufficient.
In thinking about the situation you have described with your middle school students, there are a couple things that concern me. I worry about what is underneath the reason why these students are resistant to learning strategies to help them learn to compute accurately. Are you confident that they are truly fluent using a calculator? Would they be able to explain how they are planning to use the calculator to solve a multi-step, complex problem solving task? Are your students able to explain their thinking orally well enough that you are confident they understand what the task is asking and can apply the correct math concepts to reach a solution? In that case I would say utilizing the calculator may indeed be the appropriate choice because they may be bogged down with some kind of motor coordination or organizational issue that is separate from their ability to compute fluently.
Are they resistant because of a negative attitude towards math? A friend and I just did a workshop for middle and high school teachers on motivating unmotivated students. Perhaps what you are seeing is not a learning issue at all but a lack of seeing the relevance or importance of learning math or a student’s lack of belief in his or her own capability to do math?
Another concern is around whether your students may have given up a long time ago because they have to work much harder at math than other students because they are actually doing a harder kind of math. If the only strategy a student has is some variation on counting, they have to work extremely hard to solve any math problem since counting is such an inefficient strategy. There is a very good discussion on this topic on this blog dated April 2009 around the issue of students not having good number sense. Truly, I believe this is at the root of why so many struggle at the middle and high school level.
A few years ago, I wrote an article that was published in TOMT magazine on the topic of helping students with math dyscalculia. If these were my students, I would want to spend time finding out how they are thinking through problems and about math in general before I made a decision to drop one of the IEP goals from their plan. How about the rest of you? Anyone out there who might have some other thoughts on this topic that you’d care to contribute? Are there any of you experienced middle or high school folks who could share what you do to help your students learn to compute fluently?
The March Teacher to Teacher newsletter also discusses more insight on the importance of computational fluency and how to get students to reach that goal. Click on the Teacher to Teacher link in the Blog Roll at the right to go to the Teacher to Teacher website.