Math Wars – Alan H. Schoenfeld. University of California at Berkeley

Summary

Schoenfeld raised concern about the needless math wars that went on some decades ago in the United States between the extreme reform camp who advocated for new approaches to teaching and learning math, and the extreme traditionalist camp who believed that these new approaches in teaching math will only lead to the ineligibility of students not being able to go to college. No matter how some stand to benefit from the conflict or maybe believe in these conflicts, the author believes there is a large middle ground which is sought by many teachers. He cited Daro (2003) who offers a draft “Math Wars Peace Treaty” to stay in the large middle ground.:

• ·         Teachers, especially K –8 teachers, should learn more mathematics throughout their careers;
•        No students should be denied a fair chance to learn mathematics because they have been assigned unqualified mathematics teachers. 
•        Research and evidence should be used whenever it is available to inform decisions.

Reading this article reminded me of Goldin’s (2003, p.198) ‘Dismissive Epistemologies’ (read in EDCP 550 the last term) about how detrimental these math wars among educationists (Behaviorists, Social constructivists, and Radical constructivists) can be to teachers, students and researchers. Goldin (2003, p. 198) admonishes us, “to thoughtfully reincorporate mathematical and scientific truth, objectivity, correctness, and validity, alongside other ideas, in the thinking of the mathematics education research community”.

Schoenfeld concluded that these wars have casualties – our children, who do not receive the kind of robust mathematics education they should. We should all try and get along with our diversified ideas.

Reflection

I am wondering if these math wars are still going on? Could there be such wars brewing in our own backyard (schools)?

References

Daro, P. (2003). Math wars peace treaty. Draft manuscript, available from the author.

Goldin, G. A. (2003). Developing Complex Understandings: On the Relation of Mathematics Education Research to Mathematics. Source: Educational Studies in Mathematics, Vol. 54, No. 2/3, Connecting Research, Practise, and Theory in the Development and Study of Mathematics Education (2003), pp. 171-202 

Unpackaging Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students.  – Heather. C. Hill, Deborah Loewenborg Ball & Stephen G. Schilling

Summary

·         The purpose of Hill, Ball and Schilling’s study was to understand and measure mathematical knowledge for teaching which they termed as ‘Knowledge of Content of Students’ (KCS).

• A teacher may have strong knowledge of the content but weak knowledge of how students learn the content. 
• Pedagogical knowledge deals with the teaching process which includes ways of representing and formulating the curriculum content which makes it comprehensible to the learners. 
• What happens in the classroom between teachers and students is the most important factor in determining quality in education (UNICEF, 2005: 36).  
• Hill, Ball, and Schilling concluded that familiarity with aspects of students’ mathematics thinking such as common student errors is one element of knowledge for learning.

Questions

On page 376, Hill, Ball and Schilling mentioned ‘how classroom practices of teachers changed and students learning improved when they studied how students learn the subject matter. However, it is not known whether teachers who did not partake in this professional development possess such knowledge’.

There is a controversial issue in my country between private schools (often recruit untrained teachers) and public schools (recruit trained teachers from Teacher training colleges) about academic excellence. Most people have come to accept that, students in private schools perform better than students in public schools because the teachers teach well.

• ·       Is it possible that teachers who do not necessarily go through this professional development may naturally possess or know special ways of teaching a topic(s) that may easily be understood by students, hence better performance?
• ·        Do such teachers still need professional training regardless of how well their students perform?

Reference

UNICEF. (2005) Improving quality education for children through reform of teaching and learning materials.

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

Math is fun!

Hi Everyone! Come, let's learn together.