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I received the book titled “The Math plague” last night by Dr. Sherry Mantyka (thanks Amy for dropping the book off & you and Sophie for brining Dr. Mantyka’s book to my attention). The title of the book reflects how under-achievers in mathematics feel about the subject. I started reading the book and the first 20 pages were very good – I had to put it down and put the kids to bed. I would like to read the book this weekend – if I can find the time. Next week I will be attending a meeting discussing the North Western Canadian Protocol http://www.wncp.ca/ on mathematics. We eventually will be adopting the NWCP math curriculum. I am interested in looking at the curriculum and comparing it to our existing one. More importantly I’m interested in how the curriculum outlines instructional strategies.
As I read the Math Plague I reflect back to teaching mathematics for 11 years – grade 8 – 12 math: everything from modified mathematics to Calculus. I personally believe that when teaching math, a high level of rigor is involved. Dr. Mantyka stresses drill and practice. I believe this too. My students did repeated questions until they understood the concepts and were able to apply them to application type questions. Mathematics is different from other subjects in that skills need to be learned then applied. If skills are not learned then they cannot be applied and built upon. That being said it’s all about balance. I strived to connect abstract concepts to real life problems; however I only did this where it fit. If I can talk about where the math lesson I was teaching fit to a real word application I felt it helped students. I told stories of where the math connected to real life situations, we watched videos of where the math applied, and we tackled difficult application questions, often engineering/trade-application scenarios. I always wanted to develop a math lab; however I never did – one of my regrets. My engineering and physics background at university served me well when the question came up “where will we use this?” When I taught Physics before diving into the math we had a class discussion around the concept. What is gravity? What is acceleration? Students related examples of where these concepts applied, and then we did the math. Placing the concept upfront helped with the math.
I also told students that just because you are learning math that you may not every use is not a waste of time. All mathematics can fit under the umbrella of problem solving. Students that tackle problem solving and engage the material working through it gain many valuable life skills such as critical and creative thinking, confidence, reading and word analysis.
I believe not all abstract concepts need to be grounded in a concrete example. Students need to work with abstract concepts – a reality of life. We don’t understand everything; however we do it. My children ask me “why”, my response – “because I said so”. Eventually they will get an explanation; however until I can reason with them and they have the mental and maturity to understand the response what’s the point? Eventually the development of these abstract concepts can be applied to concrete examples. (The use of the net helped me find concrete examples of many abstract concepts I had no idea of where they applied.) When I learned Calculus I didn’t know where it fit to real life – was that a problem – no - I still learned how to do it. When I took a Linear Systems and Design class in engineering I realized where many of the Calculus concepts were applied. When I took an economics and statistics class I realized where many of the Calculus concepts applied. I bridged the gap between applying mathematics concepts to other subjects. My experience raises the question about an approach to education involving interdisciplinary study. Does a restructures of our education system need to happen? Does the teaching of mathematics need to be “watered down” to include ties to real life in order to teach within the confines of expected outcomes and time? Exploring different instructional strategies within the curriculum takes time – how does this impact teaching the curriculum and student success? Again – I believe it’s about balance. We have a time frame; we have a curriculum – what can be accomplished – what’s reasonable. Don’t cut out the rigor, don’t cut out direct teaching and don’t cut out student centered learning; however strike a balance. Depending on your environment – how many students you have; what their needs are; and how much time (as a teacher) do I have for planning make up what is realistic. I had grandiose ideas of what I wanted to accomplish at the start of every year and when the daily grind of 5/5 came I was in survival mode. Obviously that impacted on my instruction. The semesters I had time to spend planning I did more innovative instruction in my class and I spent more time accessing student work with project based learning – which takes an incredible amount of time. It’s amazing what can happen when teachers have time – I see this in my colleagues work as a consultant.
Dr. Mantyka relates learning mathematics to learning music and learning how to play a sport. I watched how my 7 year old son overcame a difficult situation in swimming. His instructor was placing a lot of pressure on him to swim with more effort. My son was not a happy camper with the pressure. We supported his instructor and told him he needed to try harder. I told him to swim like a shark was behind him. Next practice he swam harder with an improved effort. His instructor told him he had improved 100%. My son was elated, he had to phone his grandparents that night and tell them. That experience taught my son a very valuable lesson. Students who try harder in mathematics and do more practice to overcome road blocks experience a sense of accomplishment. Through hard work students can build their confidence in tackling mathematics problems. As a teacher I was supportive of students who were working hard. I encouraged students to come for extra help and to do their work.
As I walk through the schools I notice math teachers working with students individually and in small groups before school, at lunch and afterschool. I know that teachers are taking time out of their personal lives to work with students; however for the students who are attending these tutorial sessions it is very beneficial to their growth in mathematics. These sessions encourage students to do their homework and to ask questions.
There are basically two ways to achieve higher completion rates in educational programs. The easiest way is to lower academic standards. The hardest way is to seek an understanding of why students under-achieve and then develop teaching/learning strategies to address these issues. [p1]
As I read Dr. Mantyka’s I will continue to blog. I hope to generate a discussion on effective ways to teach mathematics - grounded in the basis of reality. Remember that there is an ideal situation then there is reality. How can we do things better in the confines of our teaching schedule with the curriculum we are presented and the students we have.
This post was originally posted to my personal blog: http://www.jboulton.com
