Foreword for "Traditional Math" Good evidence-informed education is the new progressive!

by Paul A. Kirschner

Below is the foreword to “Traditional Math”. The foreword was written by Paul A. Kirschner.

Houston, we have a problem

Math is essential for everyone. Without being able to “do the math” you can’t understand baseball scores and its statistics (games behind, earned run average, batting average), the dosage of medicine for yourself or others (this many grams per kilogram weight), whether a bargain is really a bargain or if you’re being fooled by either advertised ‘twofer’ prices (two small bottles cost more and have less contents than one large bottle) or shrinkflation (instead of raising prices you shrink the size of the product), and so forth.

This means that math has to be taught in a way that ensures that students learn math as well as possible. In the past two or three decades we’ve seen a change. Until 1990, U.S. students were taught to solve math problems by applying memorized facts and procedures—which are significant artifacts of what we’ll call traditional math education. Since 1990 both the United States and many other countries around the world have de‑emphasized this traditional approach and stressed applying reasoning strategies over, and often instead of, acquiring knowledge and skills; let’s call this the progressive math education.

This progressive approach was first developed by the Freudenthal Institute in the Netherlands in 1971 and was given the name Realistic Mathematics Education (RME), a name still in use today. According to Yuanita, Zulnaidi, and Zakaria (2018) RME begins with the students’ daily life-experiences. These experiences are then transformed into a model of ‘reality’ that are referred to as “contexts”. The goal is to develop long-term mathematical understanding that students can make sense of. It does this through “a mathematical vertical process before turning it into a formal system” (p. 1). Put into plain English, the RME method teaches math concepts before teaching the fundamental procedures students need to achieve the goal of understanding. In RME the teacher is a facilitator – a guide on the side - who helps students solve problems in the context of mathematical concepts which its advocates assume will develop students’ mathematical representation and understanding.

This change in approach to teaching mathematics was based on the untested assumption that our brains could reason in math via concepts as effectively as it does in applying facts and algorithms that are well-organized in memory. It was therefore assumed that by making math realistic, motivational, and fun kids would and could learn better. Unfortunately, this assumption is mistaken. Research in cognitive science has shown that ‘working memory’—where information processing and problem solving occurs—is extremely limited. Because of this, reasoning that does not rely on memorized procedures and facts generally fails when solving complex problems.

The sowing of this progressive RME approach to math has reaped some shocking results. One example of this is the international test of numeracy skills by the Organisation for Economic Co-operation and Development (OECD), for citizens aged 16 to 34. In 2012, among 22 developed nations, the United States ranked 22nd and last. (Goodman et al. 2015). Why?

Though the evidence is correlational, the K-12 state math standards adopted since 1990 in the United States have changed how math is taught. With the rise in availability and use of calculators, understanding and mathematical reasoning became emphasized and memorization of facts and procedures de-emphasized. The un-noticed, unstated, untested, and optimistic assumption was made that we can reason about things without domain-specific knowledge and skills and that our brains, when solving problems, could apply new, looked up, mentally calculated at that moment, and ‘calculator calculated’ facts on a “just-in-time” basis as easily as if applying previously learned and mastered material.

Scientists who study how the brain functions when we solve problems have shown that the opposite is true, however. Working memory - where information is processed and problems are solved - has exceptional abilities to apply well-practiced math procedures (i.e., algorithms) that in turn rely on well-memorized facts (Hartman, Nelson, & Kirschner, in preparation). Research in cognitive science has identified especially efficient and effective strategies (e.g., spaced practice, interleaving, retrieval practice, overlearning) to move math facts and procedures into long-term memory so that it can be easily and accurately retrieved when necessary. In states that have aligned math standards with recommendations of cognitive research, scores on international tests have equaled and even exceeded high-ranking Japan (NCES, 2015; Hartman & Nelson 2016).

This book will, hopefully, provide an arsenal of tools and techniques to break through this downward spiral in teaching and learning math. First off, it breaks through the myth and straw man that explicit instruction (Rosenshine, 2010, 2012) is just boring chalk-and-talk rote learning of facts that cannot be applied when needed. It also breaks with the misrepresentation that traditional math teaches kids to work as automatons without understanding what they do.

Traditional is the new progressive

This so called progressive math education has been anchored in education policy, schools, teachers, teacher training colleges and courses, education trade unions, politics (and legislation) at all levels, and university educational science faculties for more than 65 years (Kirschner, 2009), It has even become a part of the education press (e.g., TES: Times Educational Supplement) in the UK.

In other words, progressive education has, slowly but surely, become the norm with ‘new’ progressive education innovations stacked on top of older innovations. And what has been the result? A continuous deterioration in pupil performance (i.e., learning) accompanied by an increase in behavior problems in the classroom (with excesses such as verbal and physical violence between pupils and against teachers).

Interestingly, teachers were blamed for these failures. It was the teacher who did not properly implement progressive education. It was the teacher who didn’t motivate the children properly. It was the teacher who couldn’t control the class. Another often used scapegoat was the environment because “what could you expect from children of low socioeconomic classes?”. This last aspect is what Robert Peal calls “the soft bigotry of low expectations” in his book (2014) Progressively worse: The burden of bad ideas in British schools.

But something that has been in place, used, and failed for more than 50 years has no right to call itself progressive. Richard Mayer (2004) spoke of the ‘three-strike rule’ when it comes to innovations that continually rebrand themselves and then prove to be just as ineffective as their predecessor. In other words, this so-called progressive education is actually traditional now, and as a result we can conclude that math education that meets the following criteria is actually new, innovative and progressive:

• It is first aimed at acquiring knowledge, after which that knowledge is used for the acquisition of skills and attitudes,

• Teaching is based on a scientific evidence-informed basis,

• Teacher training courses and teacher training colleges are given the time to as teachers teach how children learn and which learning strategies can and should best be used for this,

• The teacher is a teacher again and not a guide or facilitator,

• Children from the ‘lesser’ backgrounds are challenged instead of tolerated.

Thus, good evidence-informed math education, as the authors of this book present here, is the new progressive math education!

Paul Kirschner

Emeritus Professor of Educational Psychology - Open University of the Netherlands

Guest Professor – Thomas More University of Applied Sciences

References

Goodman, M., Sands, A., & Coley, R. (2015). America’s skills challenge: Millennials and the future. Educational Testing Service. https://www.ets.org/s/research/30079/asc-millennials-and-the-future.pdf

Hartman, J., & Nelson E. (2016). Automaticity in computation and student success in introductory physical science courses. http://arxiv.org/abs/1608.05006

Hartman, J., Nelson, E., & Kirschner (in preparation). Designing math standards in agreement with science.

Kirschner, P. A. (2009). Epistemology or pedagogy, that is the question. In S. Tobias & T. M. Duffy. Constructivist instruction: Success or failure? (pp. 144-157). Routledge. https://lexiconic.net/pedagogy/epist.pdf

Mayer R. E. (2004). Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. The American Psychologist, 59(1), 14–19. https://doi.org/10.1037/0003-066X.59.1.14

National Center for Education Statistics (2015). Trends in International Mathematics and Sciences Study (TIMSS). US Dept. of Education. http://nces.ed.gov/timss/benchmark.asp

Peal, R. (2014). Progressively Worse: The Burden of Bad Ideas in British Schools. Civitas. https://civitas.org.uk/pdf/ProgressivelyWorsePeal.pdf

Rosenshine, B. (2010) Principles of instruction. International Academy of Education, UNESCO. Geneva: International Bureau of Education. http://www.ibe.unesco.org/fileadmin/user_upload/Publications/Educational_Practices/EdPractices_21.pdf

Rosenshine, B. (2012) Principles of instruction: Research based principles that all teachers should know. American Educator. http://www.aft.org/pdfs/americaneducator/spring2012/Rosenshine.pdf

Yuanita, P., Zulnaidi, H., & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PloS one, 13(9), e0204847. https://doi.org/10.1371/journal.pone.0204847