Chinese Approach of Mastery Learning Gains Acceptance in Britain and Elsewehere
In a 5 August 2017 New York Times article by Amy Qin entitled, "Britain Turns to Chinese Textbooks to Improve Its Math Scores," found at https://www.nytimes.com/2017/08/05/world/asia/china-textbooks-britain.html the account suggests that Britain is adopting a more creative approach to teaching maths in the grade schools.
We quote from the article, " `I am confident that the steps we are taking now will ensure young people are properly prepared for further study and the 21st-century workplace, and that the too often heard phrase ‘can’t do maths’ is consigned to the past,' said Nick Gibb, the British schools minister who oversees primary education, when he announced the initiative last year.
"The teaching method, known as the `mastery' approach, is based on the idea that all students can succeed in learning mathematics when given proper instruction. Whereas teachers in the West might describe a concept and then assign problems for students to solve individually, the mastery method is more interactive."
In the mastery approach, "Teachers frequently pose questions to students who are then expected to precisely explain both solutions and underlying principles in front of their classmates." The ability to communicate to others (under scrutiny of the teacher) demonstrates a richer understanding than performance on standardized tests, but also permits better performance on these same tests. For understanding far outlasts and out performs grinding techniques and algorithmic thinking.
Here is the key point for us in SIMIODE (emphasis added), "Students learn fewer concepts under this approach, which allows them to go into those concepts in greater depth. For fractions, for example, teachers might ask students to apply the underlying principle `part of a whole' in different contexts, making use of pictorial representations and other visual techniques to explore the abstract idea. Ideally, only when the entire class has demonstrated understanding or `mastery' of one concept does the teacher move to the next."
Thus, students who move on with more understanding of fewer concepts are better served than students who gain thinner technique skills on more concepts with less understanding in each case.
The article goes on to point out that, "The movement to learn from China comes even as parents and educators in the country increase calls to overhaul the education system to ease the intense pressure on students and encourage individuality."
Further, " 'Right now, the national buzzword is creativity,' said Jiang Xueqin, a researcher at Harvard who advises Chinese schools on how to incorporate more creativity into their curriculum. `China sees it as a source of economic power, a hurdle to be jumped over to challenge American hegemony.' ”
International test scores back up the claim that the mastery approach is better and serve as part of the rationale for the British educators to adopt the Chinese approach - in translation, of course.
We see the use of understanding as a learning standard, as measured by how a student can explain the underling concepts, as significant. Indeed, applying and explaining the mathematics is the core of SIMIODE in which students can apply the concepts of differential equations to explain real world situations. Moreover, the acceptance that less is more through acknowledgment that the mastery learning approach covers fewer topics is significant. For the impediment to student learning we call "coverage" of all the topics, including useless, by-hand, and arcane techniques favored by tradition-bound faculty, especially in light of technology power to address these "olde" techniques, dissuades students from moving beyond rote and algorithmic thinking to creative applications.
Thus we concur with this mastery approach which addresses creativity (rather than rote and algorithm) while it leaves behind some topics in favor of understanding. It is what we are attempting to do in SIMIODE.