Math Myths

17 1/2 years ago, in my first year of publishing this blog, I linked to Ten Myths About Mathematics Education and Why You Shouldn't Believe Them.  Those myths are:

1. Only what students discover for themselves is truly learned.
2. Children develop a deeper understanding of mathematics and a greater sense of ownership when they are expected to invent and use their own methods for performing the basic arithmetical operations, rather than study, understand and practice the standard algorithms.
3. There are two separate and distinct ways to teach mathematics. The NCTM backed approach deepens conceptual understanding through a problem solving approach. The other teaches only arithmetic skills through drill and kill. Children don't need to spend long hours practicing and reviewing basic arithmetical operations. It's the concept that's important.
4. The math programs based on NCTM standards are better for children with learning disabilities than other approaches.
5. Urban teachers like using math programs based on NCTM standards. 
6. "Calculator use has been shown to enhance cognitive gains in areas that include number sense, conceptual development, and visualization. Such gains can empower and motivate all teachers and students to engage in richer problem-solving activities." (NCTM Position Statement)
7. The reason other countries do better on international math tests like TIMSS and PISA is that those countries select test takers only from a group of the top performers.
8. Math concepts are best understood and mastered when presented "in context"; in that way, the underlying math concept will follow automatically.
9. NCTM math reform reflects the programs and practices in higher performing nations.
10. Research shows NCTM programs are effective.

How far have we come since then?  Not far at all:

In this paper, leading education researchers Sarah Powell, Elizabeth Hughes and Corey Peltier debunk seven commonly-held myths about teaching maths – (1) conceptual then procedural understanding, (2) teaching algorithms is harmful, (3) inquiry learning is the best approach, (4) productive struggle is important, (5) growth mindset increases achievement, (6) executive function training is important, and (7) timed assessments cause mathematics anxiety.

Myths That Undermine Maths Teaching

I don't want to ascribe hostile ulterior motives to teachers who believe any of those 17 myths listed above, but they're teaching other people's children with those views.  At some point you have to wonder.