Unit Plan for Math 10 Systems of Linear Equations

Unit Plan

Response - John Mason: Questioning in Mathematics Education

1) Do Mason's ideas connect with inquiry-based learning in secondary school mathematics? (And why or why not?)
2) How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?

After reading John Mason's article, I think his ideas connect with inquiry-based learning in the secondary math classroom. The majority of the questions that I had often heard from my high school teachers and ask students myself are in the category of "asking as telling" which directs student attention to easier and easier answers. This type of questioning is not very helpful for student to genuinely learn to think mathematically. I was impressed by how Mason articulates the form of "teaching by listening" in that the teacher is not listening for an expected answer but listening to student's thought process and how they might justify their answers. Eventually, students internalize the metacognitive-type of questions about their own solutions so that they are capable of thinking mathematically without the teacher's verbal prompts.

In my planning for long practicum, I will try to incorporate time to interacting with students during lessons. I will write in questions such as, "How do you know...?" and "Will that always be the case?" I want to encourage students to articulate what they understand rather than being fearful of responding incorrectly to my questions. For a formative or summative assessment task, I will have students construct and solve their own problems, even ones that will challenge their peers. As a teacher, I will model the mathematical thinking myself by not immediately asking funnel-oriented questions or supplying answers but asking, "What did you do yesterday when you were stuck?"

Reflection on group micro-teaching

We did well in terms of time management and organization of the lesson parts. I think this group micro-teaching lesson shows much room for improvement. The beginning of the lesson and the hook were not demonstrated clearly. I would bring in some visuals such as ads from magazines that show percentages to relate the lesson to everyday life. The lesson development or examples of problems were good but I feel they could be more student-centered. Perhaps, the calculations can be some certain characteristics taken from the group of students so they will feel more involved. I think the activity went pretty well as students were interested to find out predictions of their lifespan. Also, we were able to generate further follow-up questions for discussion to make up the remaining time. See pictures of peer- and self-evaluation forms here.

Group micro-teaching lesson plan

Teachers: Jessica, Mandeep, Simran

Topic	Intro to Percentages
Grade level	8
PLO	A3 demonstrate an understanding of percents greater than or equal to 0%
Objective	Students will be able to use the given percentage to find the required information. Students will be able to find percentage of two given whole numbers. Students will have the understanding of the percentage sign.
Materials	White board and marker. Lifespan cards.
Prior Knowledge	Students know division and multiplication.
Intro/Hook	4 mins	Percentage sign %, no calculations here. Discuss how many pennies make up a dollar. (nickels, dimes, quarters). Each group still represents one dollar. On the board, draw out a circle representing a dollar and then fill in 25% to represent 1 quarter.
Development	4 mins	Finding a percent of any number with respect to another number (comparative number) Here percent represent the fraction with denominator 100,While the number represent the amount. Example1 -  if i have 40  halloween  candies ,i gave  10 % of candies to my son ,then what is the number of  candies i gave to my son? Solution- Here, 40 is comparative number    10% of 40 candies = 10/100* 40 =  4 candies to my son Example 2-   If i have 40 halloween candies ,i gave 10 to my daughter,then what is the percentage of the candies i gave to my daughter? Solution-       10/40*100 =25 % of  the total number of candies to my daughter
Activity	3 mins	-Give each student a “Lifespan” card - Ask them to fill out the blanks on the card, their age etc - Explain the question on the card and tell them to do their calculations on the back of the card - let the students work in pairs of two for 2 minutes - go around and make sure everyone's clear on the activity
Closure	1 min	go over the idea of percentage and how it can be used in daily life. For ex: at the shopping mall, calculating the time you have left before you have to get ready for school or dividing your food into portions and eat a certain percentage at a time. It becomes very easy to picture what's gone and what's left if you convert things into percentage.

2-column solution to "Thinking Mathematically" puzzle

Exit slip: video of Dave Hewitt's math classes

Watching the videos of two of Dave Hewitt's classroom caused me to think about my own style of teaching, what my goals of each math lesson should focus on, and students' response to a lesson. I like how Mr. Hewitt utilized the entire perimeter of the classroom; the shift in orientation with regards to each student benefits student attention. Also, I was impressed at how extensively repetitions were used to emphasize the main points. Another area of interest was the choral response from the students since most of the time, I imagine a math classroom to be mostly quiet with either the teacher or one student speaking. I think the choral response is generally a good approach but I would like to check the answers at some point. A student may have said a different answer than his peers but maintain that his was correct. The second lesson in which Mr. Hewitt introduced the idea of variables and different operations was quite interesting as well. I think how he subtly wrote down "x" while saying "I'm thinking of a number" was a great way to express these equivalent relations to students.

Response - Dave Hewitt: Arbitrary and Necessary

Arbitrary is something that cannot be worked out. It is in the realm of memory where students must be informed of this information. A square can just as well be named a "syervel" or any other name. There does not seem to be a definite reason why it is named a "square". Such knowledge is arbitrary.

Necessary is something that can be worked out. Students can use their awareness or prior understanding to figure out a mathematical fact. For example, they can determine the position of a quarter-turn and a half-turn in reference to some point of origin.

For a math lesson, the larger part of the time allotment should focus on working out the necessary mathematics. Less time should be spent on practicing the arbitrary. This influences my lesson plans in that the teacher should have a shorter amount of time talking about what is arbitrary: the names, symbols, notations, and conventions, and the students would have the guidance to work out what is necessary: the properties and relationships in mathematics.