Reflection of Battleground Schools

 In this book I learnt about how mathematics education has shifted between progressivist and conservatives since 1900. In the conservative stance, mathematics is seen as a stable, objective and cold truths that exist independently of human experiences. Students are expected to memorize the definition and procedure, and practice over and over again in order to produce the correct answer. The approach disregards the deeper meaning of mathematics and, more importantly, the intellectual and creative growth of students. This is contradicted to Lockhard's perspectives that "mathematics is the purest of the arts." He also points out that "math is wondering, playing, amusing yourself with your imagination." suggesting that mathematics should be an act of exploration and creative expression. Through this way, students can discover patterns, make new connections, and sustain their enthusiasm for mathematics.

I highly agree with John Dewey's perspective of "proposing that students must engage in doing mathematics as part of reflection inquiry if they were to increase their intelligence and gain knowledge." , which was a truly forward-thinking idea. Even though inquiry might bring more uncertainties into the class that may not align perfectly with what the teachers intend to deliver, it maintain one of the most effective approaches to nurture students' "sense of mathematics". For me, I found it is interesting and challenging to do some hands-on mathematical activities when i was a student, as it allowed me to gain deeper insights through active thinking. In a 80-minute class, merely listening to teacher without any physical or cognitive engagement makes it nearly impossible for students to stay focused or meaningfully gain knowledge. Dewey's advocacy also reminds me of the concept of "de-fronting classroom", which encourages student thinking and autonomy. Teacher who choose to de-front their classrooms commit to giving students more authority. In such inquiry-based classroom, more thinking, collaboration and risk taking are expected.

The "New Math" movement if the 1960s was aimed at improving the nation's scientific competitiveness. It  shocked me that the Bourbaki group set the university mathematics topics to be taught throughout the K-12 system. Concepts such as set theory and symbolic logic were far beyond what many students and teachers could meaningfully grasp at those levels. This misalignment between content and learners’ developmental level led to confusion and frustration for not only the students but their parents. As I can imagine, as a result, many students became demotivated and felt pointless to be in mathematics classroom. Moreover, it is always important to set a clear and realistic goals for students, as having attainable objectives allows them to track their progress and stay motivated throughout the learning process.