Reflection on "Three 20th century reform movements in mathematics education"

Here is a brief list that contains all the big issues mentioned in the article. All items are categorized into three different eras:

Progressive Reform (1910-1940)

• Early days of public school in NA 
• Criticisms of school math as a process of meaningless memorized procedures
• Targeted on memorizing rules than understanding the meanings 
• Cares more on answers than reasons
• Alternate ways are ignored
• Push for quick, correct answers and a short circuiting of uncertainty and doubt

• Reform addressed to unify algebra and geometry and to bring both pure and applied math to the secondary school
• Addressed the nature of mathematics teaching and learning and questioned the concept of covering topics
• John Dewey proposed that students must engage in doing math as part of reflective inquiry if they were to increase their intelligence and gain knowledge
• Process of experimentation and inquiry was difficult to control than simply lecturing to large groups
• Students need challenge of doing and experimentation in math
• Sense-making activities of reflective practice
• High quality mental processes and scientific attitude
• Problematic and a degree of uncertainty as the incentive to form and test hypotheses and perceive patterns and relationships

The New Math (1960s)

• National anxieties in US 
• School math was not keeping pace with changes in research-level math at universities 
•  US face a shortage of qualified college students 
•  New math 
•  Inclusion of modern math areas in school math 
•  Set theory, abstract algebra, linear algebra, calculus, etc 
•  Regardless of local conditions, cultures, or educational traditions in other countries 
•  Imposed western, collegiate, highly abstract math in school

-          Early 1970s, new math was being denounced

• Misguided experiment 
•  Similarity to the progressive:

o   Inquiry and sense-making over absorbing and applying facts

• Differences:

o   Conservative as university teaching

o   Presentation, precision and correctness

o   Deductive method than others

o   Math is infallible and authoritative

o   Individual tests

o   Knowledge was assumed to be in the head of learners;

o   Aim to produce teacher-proof materials that could be delivered by teachers anywhere in the world

o   Aim to educate future elite scientists and mathematicians but refused the rest students

Math Wars over the NCTM Standards (1990s - present)

• Back-to-basics curriculum, standardized tests, rein-in of teachers’ autonomy in the name of accountability 
•  NCTM standards 
•  Flexible problem-solving skills 
•  To present math relationships in multiple forms 
•  Emergent technologies like graphing calculators and personal computers 
•  To communicate mathematically 
•  Appreciation for the power and beauty of math 
•  Depth of understanding 
•  Make math connections above calculation skills 
•  Although fluency in calculation was still considered an important goal 
•  Different opinions 
• Anxieties

o   3^rd TIMSS: bad result (28^th) of US math

o   Deeper conceptual understanding of math was key

o   Continuing

Comments:

    The old style of teaching in that era was “appropriate” in the era before. With limited educational resources and “low” need for most kids to understand mathematics, mathematics education tended to put more efforts on calculation and procedures so that graduates can perform basic works in factories. During WWI and WWII, more and more mathematics knowledge was applied in arms and wars (and of course in factories and almost all the industries), requirements for workers were raised correspondingly. The old-style products could not perform well in the changing environments. Thus educational reform became a necessity.

    But, why was Dewey? A simple answer could be the mainstream social values required a sound like Dewey that emphasized individual values and developments, especially at the time the world war was over and everyone returned to a relatively peaceful environment. The problem was that the cost of implementing Dewey’s educational methods was (and still is) so high that it was almost unrealistic for most families (in the US, not to mention the world).

    Similar situation happened in the NEW MATH era and the concurrent MATH WARS and NCTM STANDARDS era. Teachers and schools are not the elements in society which stay in the first line of use new knowledge. Therefore, they cannot be the first one who calls for changes. It is not surprised to me that all these reforms were not first advocated by teachers. 

    Then can teachers become the early birds in the next reform? 

    The current situation of use of mathematics in industries is extremely polarized. On one side, only a proportion (vary based on industries) of high-school mathematics knowledge is largely used; on the other side, high-school-and-university-level mathematics can only be a small component of a qualified worker’s knowledge base: other related knowledge like statistics, economics, accounting, physics, chemistry, biology, and so on, are the necessities that support the worker.

    Then, what is the matter here? My answer is the ability to learn (and communicate, but this is of topic so I would not elaborate it here). Learning from problem solving is important, but self-learning through reading and analyzing should be placed at a higher rank. In my case, I would encourage students to read textbooks as a daily pre-reading assignment, so that I would have more class time for solving problems and exploring ex-curricula relevant topics.

I should have elaborated the last paragraph more about the logic of self-learning and reading. I would improve this article in a weekly basis and see how I reflect myself every week.