EDCP 342 course reflection

EDCP 342 was an amazing course, and I had so much fun learning about mathematics curriculum and pedagogy. I learned about school institutions and the evolution of mathematics through the ages beginning with the progressivist movement led by John Dewey, to New Math reform of the 1960s and to current math practices beginning the 1990s.

One of my favourite readings was Eisner’s Three Curricula that all schools teach as it discusses the implicit curriculum that students learn in school and is not explicitly listed in the official teaching curriculum. These remind me of the “life lessons” or “life skills” that usually come up in my elective courses in home economics and automotive, but also appear in academics unintentionally.

Being exposed to the different aspects of the BC curriculum such as core competencies and big ideas are very helpful from Susan’s guidance and microteaching activities as it got us thinking about ways to incorporate different elements of these goals into teaching and developing lesson plans. This has changed my ideas that every unit has to include all aspects of big ideas/core competencies, when in fact different units may be easier to promote different big ideas/core competencies. For example, in my unit plan assignment on data analysis for Math 9, I found it to be a great unit for developing mathematical communication and reflection rather than specifically focusing on mathematical computation.

I also enjoyed the discussion on Csikszentmihalyi’s idea of flow. It got me thinking about ways to develop lessons that promote focus and concentration while also submersing students into a sense of timelessness.

A suggestion I have for improving the course next year, would be to consider reducing the number of assignments so that there can be more time for reflection and stronger development of ideas from multiple draft review opportunities. Towards the end of the course after the short practicum, there have been several instances where I felt rushed to complete assignments such as this unit plan. Nonetheless, this was an amazing course and I am very thankful to have such a caring and knowledgeable instructor like Susan to teach this course.

 

Thank you, Susan.

Completed Assignment 3

See the link to my google drive for my completed unit plans.

https://drive.google.com/drive/folders/103f3B4C9PUc2OgapEh_gF6G93jzfBbXz?usp=sharing

Math Party

My friend and colleague, Curtis Chou, has a great thought mathematical thought experiment regarding the Mobius Strip that I would like to share with everyone.

Curtis Chou Returns to Science Slam Vancouver - YouTube

I also just realized that in a non-covid year, December is typically a time where PE classes do square dancing and I just wanted to share a few resources of embodied math and square dancing. 

https://www.maa.org/news/math-news/square-dancing-takes-a-mathematical-spin

https://eric.ed.gov/?id=EJ972388

Assignment 3 Lesson Plans Draft

 

See the link to my google drive for my draft lesson plans.

https://drive.google.com/drive/folders/103f3B4C9PUc2OgapEh_gF6G93jzfBbXz?usp=sharing

Dave Hewitt on Arbitrary vs. Necessary

 

Hewitt refers to the ‘arbitrary’ if it is something that students need to be informed by someone else and is concerned with names and conventions that students have to memorize (1999). It is the role of the teacher to assist students with retrieving this information through memory. The ‘necessary’ is something students can become aware of without being informed by someone else (1999). The teacher should provide tasks to help students educate their awareness to the arbitrary.

Thinking about this distinction between arbitrary and necessary will help me plan my lessons and develop as a teacher with regards to how I teach. Hewitt refers to ‘received wisdom’ as the fact given to students by the teacher and perceived by the student to be true as a result (1999). For example, when learning about the order of operations, students are told about BEDMAS OR PEDMAS by the teacher, which is an acronym reminding students the order they should perform arithmetic operations. If a student does not memorize this acronym, then they will incorrectly solve order of operation algebra problems. Even myself, I do not know why this order is the standard, but it is the agreed upon convention used everywhere. One of the points Hewitt makes that stands out to me is to give students time to use their own intelligence to become aware of why certain procedures must give certain answers instead of constantly giving them teacher’s wisdom. For example, when determining the area of a rectangle, students first must be told the definition of the area, and then be given the opportunity to “discover” how they can determine the area before being told the equation for finding the area. This allows for self-discovery before immediately being told the equation and eliminates the big question of “why is this the equation the area of a rectangle?”

 

Reading:

Hewitt, D. (1999). Arbitrary and Necessary Part 1: A way of viewing the mathematics curriculum. For the Learning of Mathematics, 19:3, 2-9.

Teaching Perspective Self-Test Results

This is the result I got from my TPI graph. It appears my nurturing perspective is a dominant feature, while apprenticeship is just above the mean and social reform just below the mean. Transmission and developmental are both almost recessive traits according to this test.

I am not surprised that nurturing is a beyond exceeding trait for myself as I often find myself being a very caring person and focused on social and emotional wellbeing of others as well. I was surprised at how apprenticeship was a little above the mean. Apprenticeship refers to teachers being able to know what learners are capable of and where they may need guidance. As teachers mature and become more competent, the teacher role changes and may offer less direction and give more responsibility to students (Pratt & Collins, 2002, p.3). When educating students, I like to let them ‘struggle’ a little bit when solving problems rather than giving them the answer immediately. The development was also not a surprise. Pratt & Collins (2002) refer to developmental as effective teaching planned and conducted “from the learner’s point of view” (p. 4). During my practicum, I noticed that I was sometimes explaining concepts a little more advanced than my students could understand; likely due to my additional knowledge coming from post-secondary math experience. It is important that as an educator, I teach concepts that could be understood by my students at a level to their understanding.

Given this information provided from the TPI test, I am curious to see how my results change after a few years of teaching and whether or not I will still score the same results. I hope to still score high on nurturing aspect, as I believe that one of the first avenues towards making math fun, is for the students to see that through a caring and passionate individual.

 

Source:

Pratt, D., Collins, J. (2002). Summary of Five Perspectives on ‘Good Teaching.’ TPI – Teaching Perspectives Inventory.

Thinking about math textbooks

As a student, I personally enjoy having textbooks as alternate sources of information to supplement teacher instruction. I also find that I greatly benefit from questions in textbooks to practice my understanding and refer to sample worked out questions if I need clarification. Comparing my answer with the textbook answer helped solidify my understanding of the material. From the teacher-bird view during my two-week practicum experience, all of the teacher I met referred to the textbook for practice questions, but did not know what questions were off the top of the head; when students asked, “I don’t understand question 9” or “Can you help me with question 18” teachers needed students to read out the question or refer to their teacher solution handbook before attempting to help. This changed my perception of how teachers use textbooks. When first developing lessons, they refer to textbook as sources of information and find relevant questions to assign students; then over the years, they may not refer back to the textbook unless they need clarification or a quick review.

I believe that textbooks are extremely valuable resources, however, I do not agree with having students to spend hundreds of dollars for new texts. An example of this is with booklists in post-secondary courses; students are required to purchase specific texts as described by the instructor. The Math department at UBC is doing a fantastic job towards making textbooks electronic and free to access. This would be an excellent idea for secondary schools to try and implement; to make education more accessible, especially if the school is in an area where many students have financial hardships.

In Herbel-Eisenmann & Wagner (2007), the discussion on how the textbook authors use pronouns to address the reader is something I resonate with. I enjoy reading a book where I feel a more personalized connection with the author. Hence, when a math textbook uses first person pronouns such as “I” and “we”, I feel more drawn in and connected to the learning experience. When an author uses third person or phrases like, “one can see that…” I feel more disconnected and almost feel talked down upon. Therefore, although a textbook can be helpful to students to learn by providing supplementary content and practice problems, it may not effectively achieve this if the language within is not welcoming.

 

Reading: Herbel-Eisenmann, B., Wagner, D. (2007). A Framework for Uncovering the Way a Textbook May Position the Mathematics Learner, For the Learning of Mathematics, 27:2, 8-14.