Mathematics teaching, as a cognitive tool, my goal in teaching this disciplinary is to help shape student original views through introducing a framework of the testimony summarized from our practical mathematics learning experience so that the cognitive learning can be visible to students through a deductive learning process. Under the circumstance, students learn to grab knowledge facts, comprehend and interpret the conceptual components, then apply what about their understanding to context. During the process of learning where their original knowledge system has been shaped as adding new knowledge and requiring new skills through implementing process of assimilation and accommodation. Our teachers, working as a role of knowledge spreading mediator, take the responsibility to help students accomplish the transformation in a process of closing the gap between the behaviorism and constructivism on knowledge and skills learning due to the cognitive deficit.
Three testimonies below help support the statements above.
Jo Boaler[1] (2002) believes math teaching benefits students to learn to deal with the relationship among knowledge, practice and identity from math learning activities. Interactive classroom teaching through class discussion, proposal’s theories, critical thinking and problem-solving shed the light on the idea of dance of agency where students can work as their own math agency to exchange ideas of math learning associated with the standard methods they are taught.
A video about Bloom’s testimony from Professor Lue in Harvard University suggests the need of developing our own learning models to the best of fit to the needs of our students rather than following a standard one. To this point, since students come from various levels out of our control, it is challenging if I have only one model in mind while teaching students who are with diversity from all aspects
For example, when teaching topic of The Division of Whole Number [2], looking at the learning testimonial to developmental level college students, we don’t need to doubt students who don’t understand multiplication rule will have difficulty in working on division problems as it is derived from multiplication rule. However, to have students establish the algorithm of division, a successful transformation from the multiplication and from the real-world models to the division is necessary. Students are expected to apply to real world problems where they can build up a division model.
References:
[1] Jo Boaler, In For The Learning of Mathematics, 2002, 22 (1), 42-47
[2] Precalculus, Openstax
