David Tall - Discussion

Teachers as mentors to encourage both power and simplicity in active mathematical learning -David Tall

Summary

David Tall elaborated on several ways teachers could adapt to make mathematics quite easy and enjoyable for students. Most students are anxious about the subject and Tall believes that it is the responsibility of the teacher to make it appear simple to the students. He listed the following as simple ways of encouraging students in active mathematical learning.

1.   Compressing knowledge. Being able to compress mathematical knowledge is “one of the real joys of mathematics”. (Thurston, 1990, p. 847 as cited in Tall, 2004.)

2.   Symbols as procepts is also a simple way to guide students to be flexible with numbers (decomposing and recomposing).

3.   Guiding students to identify different ways of interpreting symbols.

4.   Linking embodiment and symbolism

5.   Making connections in the classroom.

A connectionist classroom is ideal in helping students recognize their potentials in math. This seems to resonate with Skemp’s (1976) idea of relational teaching of mathematics, in-depth teaching of mathematical concepts, meaning making and making connections to the real world for a better understanding of concepts. However, I think a bit of the traditional transmission approach in the class may be fine. What do you guys think?

I recently met a seventy-five-year-old man at Safeway, MacDonald who pursued Chemistry at UBC. After revealing my program to him, he was quick to add that “Canada is always changing the ways of teaching mathematics, yet children cannot do simple calculations without resorting to the calculator. I do not know what’s happening”, he said.  I asked how he was taught, and he mentioned drills with a firm teacher. It seems our seniors still prefer the traditional transmission approach.

Also, I think the use of either of these approaches in the class depends on the topic on board.

Tall made mentioned that, “Imposed targets in many countries press teachers to train their students to obtain higher marks on national tests.”

In EDCP 550 last term, I read about this issue by Jo Boaler (2015) in her book, ‘What’s math got to do with it?’ Here, the author raised concern about standardized testing which harms teaching and learning. She quoted, “Almost every mathematics teacher in America will tell you that the pressure to prepare students for standardized tests harms their teaching and their students’ learning” (p. 87).  For instance, my country’s school curriculum is very much exam based which put a lot of pressure on teachers to teach students to pass national exams.

However, I was also wondering that teachers are mostly measured by how well students perform (at least in my country) in tests and not in tests. How are we to save our faces or avoid being sacked because our students failed than to teach for exams? These national tests are to usher students into the next level of their academic life and therefore teachers need to help them to pass. In my opinion, I do not see these targets as imposed but a form of motivation to best teach students to understand the concepts and to pass exams. It is also a way to ensure accountability on the part of teachers.

Reflection: In your opinion, do you think these set targets are imposed on teachers?

References:

Boaler, J. (2015).  What’s Math Got To Do With It? Published by the Penguin Group (USA) LLC, New York

Skemp, R. R. (1976).  Relational Understanding and Instrumental Understanding. Source: Mathematics Teaching in the Middle School, Vol. 12, No. 2 (SEPTEMBER 2006), pp. 88-95. Published by: National Council of Teachers of Mathematics