Lesson Plan for Group Curricular Microteaching

 Lesson Topic: Operations with polynomials of degree less than or equal to 2

Names: Elvie, Hannah, JJ, and Tiffany

Subject: Mathematics      Grade: 9

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Learning Outcomes: 

• To learn key terms and notation for polynomials

• To be able to recognize, add, and subtract different polynomials

Materials:

• Multimodal slides on polynomials

• “Check Your Understanding” Kahoot exit ticket

Hook/Intro:

• Has anyone heard of polynomials before? If so, what do you already know? What do you still wonder?

Lesson Structure:

Introduction (1-2 minutes)

• Short discussion about hook questions to gage what students might already know

• Briefly introduce the topic and the shape of the day using the slides

Key Terms (3 minutes)

• Go over definitions of the following terms from the slides:
  - Polynomial
  - Degree
  - Coefficient
  - Constant

• Pause and ask if anyone has any questions so far

Types of Polynomials (2 minutes)

• Explain the difference between monomials, binomials, and trinomials

• Go over examples from the slides

Adding and Subtracting Polynomials (3 minutes)

• Discuss the meaning of “like terms”

• Show how to add and subtract polynomials with examples from the slides

Check Your Understanding (5 minutes)

• Pause and ask if students have any questions and address accordingly

• Facilitate class Kahoot 

• Circulate and observe how students are doing with the questions

Extension: 

• Factorization and multiplication of polynomials

• Go over examples in the slides with the students if there is time leftover

Adaptations:

• A quick background knowledge check if students are familiar with mathematical language like variables, terms, and exponent. 

• If students want more visual representations or struggle with abstract concepts, we can guide them to resources like Desmos, GeoGebra, and online interactive algebra tiles.

 

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.

Reflection to Lockhart’s Lament

The example of music and painting education in A Mathematician’s Lament reminds me of a poem I recently read called The Little Boy. In the poem, a young boy is in his painting class, where the teacher dictates every step of the process. The teacher controls when the students may begin, which colors of crayons they must use, and even what subject they should draw. Even when the chosen theme is something as simple as “dishes,” the teacher restricts the size and shape of the dishes. Under such rigid instruction, the boy is “manipulated” into suppressing his imagination and curiosity. Later, when he transfers to another school where creativity is encouraged, he struggles to break free from these limitations. He has already become accustomed to listening carefully for what the teacher wants and cautiously following the rules, instead of expressing his own ideas. 

I highly agree with the Lockhart's idea that what really need to be done to improve education situation is to hear from our students. This aligns with building an inquiry-based classroom, and it also enhances students' creativity and curiosity. As Lockhart describe, mathematics should involve "wondering, playing, amusing yourself with your imagination." As a teacher, we should leave a big enough space to students to imagine, experience and play with mathematics concept just like how art teacher should give students freedom to create their own paintings. In this process, the teacher becomes a guide and supporter rather than a strict director.

Lockhart criticizes about the giving directions in learning math without discovering by themselves. However, in Skemp's article, he argued about relational understanding and instrumental understanding that both of them has advantages. Skemp acknowledges that instrumental learning can have benefits, such as giving students immediate success and confidence, and sometimes serving as a stepping stone toward relational understanding. At this case, while Lockhart argues rigid direction is largely harmful to students, Skemp suggests that even instrumental learning has potential value when used appropriately.

Revised Lesson Plan and Reflection

 

Date: Sep 30th	Title: Master Golf Rules with PGA Standards
Lesson duration	15min
Big Ideas, Competencies, and Content	Introduce Golf rules with PGA standards Scoring terms and meanings
Learning Objectives   (SWBAT … The student will  be able to…)	Understand the game design and key scoring terms. Be able to watch a golf competition and engage with it from their own point of view
	PROCEDURE
Elements of the lesson	Estimated Time	What the teacher says/does	What the students do	Material
Introduction	1min	“Have you ever seen golf on TV or in movies? What did you notice? “	Small discussion with other people	slides
Body Activities	2min	Introduce the essential rules of golf How scores work in golf	Can come up with different questions	slides
Body Activity	4min	Scoring terms and meanings Giving specific scenarios and discuss in group or individual	Can come up with different questions Think, pair, share	slides
Closure	3min	Exit ticket Giving a few true/false questions for students to answer	Think, pair, share	slides
Student Assessment	-	Self-assessment Peer reviews	Self-assessment Peer reviews
Plan "B"		Talk about some real-life experience and hold discussions

Reflections:

1. Make sure the materials are all correct and accurate. （I mistakenly switched two scoring term examples in my slides）

2. Need to improve on time-management, leave some time for student questions and properly organizing the 10 minutes.

3. Prepare a hands-on activities. (where i will add different scenarios for students to apply the rule in real life examples.)

4. Course content should be better tailored to the level and background of the target students.

5. Exit ticket questions could be more challenging, as most students were able to answer them correctly this time.