John Masons's Questioning in Math Education Reflection

I really like the idea of Japan's culture of asking "in how many ways can you solve the problem?". It's so much less structured and rigid than in Canadian schools and it promotes the freedom and creativity of mathematics. This lack of boundaries directly supports inquiry in the classroom.

I firmly agree with the complexity-oriented approach to pedagogy. Believing that your students are intellectually capable enough to attack a problem with little to know guidance is the foundation of what an inquiry-based classroom needs to succeed.

Carefully choosing constraints, not being too frequent, infrequent, or intrusive in my interventions, and creating an environment in which I am not the gauge of correctness in the classroom but the student themselves is a great way to foster an inquiry-based classroom. Building a conjecture-based classroom is something that really appeals to me, where "everything said needs to be tested and justified". I need to encourage students to ask questions and I need to be okay with not knowing the answers, and further, be okay with letting students know that I may not know the answer. I think this fosters an inquiry-based classroom as well as a trusting environment for students and myself.

To this end, inn my unit planning, I could build in a "question of the day" part of my lesson or my week where I simply open a discussion up to the class about a math concept that I may be unsure about or that has come up in the lessons during the week. This would promote good, relevant questioning and create a culture in the classroom that is trusting and inquiry-based.

Group Microteaching Self-Reflection!

I think our presentation went great! The common theme in the feedback from other students (and something we noticed as well) was that we needed more assessment of student learning. While we did get continual feedback through student interaction/responses during the lesson, we had no time for individual work to check if everyone understood the concepts. This leads to a timing aspect, we had many questions from the students during the lesson and quickly ran out of time for the individual work we had planned.

All in all, everyone loved the activity and appreciated our efforts to make linear relations more interesting through the use of drama and wizardry!

Group Microteaching!

Two Column Solution

Linear Relations Lesson Plan

Linear Relations Lesson Plan

Subject: Mathematics Grade:    8	Lesson Number:    7  of  8 Time: 15 minutes
Big Idea or Question for the Lesson: What is an ordered pair? What is a linear relation?
PLO foci for this lesson: B1 graph and analyse two-variable linear relations [C, ME, PS, R, T, V]
Objectives: Students will be able to  (SWBATs) determine the missing value in an ordered pair for a given equation create a table of values by substituting values for a variable in the equation of a given linear relation describe the relationship between the variables of a given graph construct a graph from the equation of a given linear relation (limited to discrete data)
Content and Language Objectives: -   understand what an ordered pair is (verbal) -  determine what a linear relation is (verbal/kinesthetic)		Skills/Strategies required: -  understand what a variable represents -  be able to solve for a variable in a given equation
Materials/resources: masking tape sharpie/thick pen whiteboard/markers Graph paper to hand to students
Assessment Plan: formative assessment: visually see if the students graphed their ordered pair correctly
Adaptations: [ for EALs] just make sure when you say, “variable”, you point specifically to the variable, and same goes for any integers skeleton note sheet that they fill in at the end of the lesson Modifications: [for slower processors] skeleton note sheet that they fill in at the end of the lesson Extensions: [ for the ‘quick study’ folk] graphing negative slopes, or more complicated functions (individually on their own graph paper)
Hook and Introduction (2 min) (__:__ - __:__) PREPARE THE FLOOR! review that they know what variables are and such hook for full lesson (graph “spicy vs parachute” ask Alison) Development (about 15 min) (__:__ - __:__) - Teacher-led (10 min) (__:__ - __:__) - Class/Group Activity (__:__ - __:__) Ian: Today we are going to look at linear relations (draw on board). Everyone should pair up and tell everyone to pick an integer from -3 to 3 but you cannot repeat a number that someone else chose (throw the stuffy at them as they choose). An evil wizard kidnaps your stuffy. He locks your animal in a dungeon. You need to rescue it! But you don’t know where they are. Alison: You only are given two clues: (1) your stuffy’s cell number (x-coordinate), which is the number they chose, and (2) a cipher that represents a map of where all the cells are (explain this). Find your animal by finding the y-coordinate of its cell. Ian: This wizard has bamboozled us! Let’s try and figure out how to use this cypher. Take a look at this grid below us. This line is labelled x. Let’s all find our places on the x number line and place your stuffys there for now. Because this dungeon is this whole grid, we have this up down or y direction. In order to find out where your cell and your animal is in the y direction, we must find our y values! How can we do this?! Questions: how can you find the y coordinate using your x value? How can you show this visually on the map/grid of the evil wizard’s lair? What order should we rescue the animals so we’re the fastest? Now give students time to solve for their y value, and place their stuffy on the grid taped to the floor where they think their cell is Alison: Now open up a discussion of what the shape of the graph looks like, because it’s actually continuous between each person (object). Hint: It’s a straight line. It’s a straight line! So! What does the class think Linear means? If this equation is a two variable LINEAR equation, and it comes up with a straight line, thennnn!’ So each of you has an x value that you chose, and a y value that you figured out using the equation we gave you. What you did when you got those two values is figured out an ordered pair. Conventionally, we write it as such (x,y). This is arbitrary.Get everyone to represent their coordinates as ordered pairs, and then collect them all on the board. Now… level two! Independent Work (  :   )-( :  ) (5 mins) Ian: Move to independent work, now LEVEL 2! You are now all kidnapped and placed in new cells!  But now you have a different cipher to figure out where everyone’s animals are (cell numbers are -3 to 3)! (Hand out the ciphers as scrolls) Create a list of ordered pairs (like we did on the board) and then plot them on graph paper (individually). cipher: y= -3x+2 Hand out graph paper, scrolls, and have students create a list of ordered pairs to figure out where everyone else’s cells are (with x values -3 to 3) and then plot them on the graph paper (figure out their y values). Closing (1 min) (__:__ - __:__) Now we all know what linear means and how to graph when given an x value! Could you figure the graph out if given a y value? ALSO DO YOUR HOMEWORK!

Brief Review of David Hewitt's In Class Methods

Adding and subtract whole numbers:
I thought this was a great use of classroom space, a great way to keep students engaged (as they clearly were), and the choral speaking was an inspiring way to get instant feedback if everyone is understanding or not.

I'm Thinking Of A Number:
This was so brilliant; such an elegant way of teaching about solving one variable equations. Posing it the way he did made it seem like a magic trick, or a game, so students were immediately interested and consistently engaged. His syncing of his words and what he wrote down was a great way to use both visual and audio cues to teach. He also used repetition fairly frequently, which I think benefited this particular strategy very much. I loved it. I am absolutely going to use this (or a modified version of it) when I teach algebra during my long practicum.

SNAP Fair Review

This was taken from an email I wrote to the organizer of the SNAP Math Fair, it is slightly editted to change pronouns etc:

Great job with the SNAP fair today! It was really great and the students were so enthusiastic about their projects! I think it really goes to show how far [the organizers have] gone in terms of student centered approach. [The students] took such pride and ownership of their set up, presentation, and location in terms of their choice of Anthropology exhibit. I had several students tell me to "Go check out this person's presentation, you'll love it", clear example of how non-competitive and, in fact, celebratory this fair is. Students were just so enthusiastic about the math. The all-inclusive aspect was great as all types of mathematicians could be represented in their problems: logic, patterns, relations, arithmetic etc. And I didn't even get to see them all! The problem based approach is such a great avenue for students to explore problems that they love and gave me great ideas for puzzles to use in my classroom, which is just so exciting for me!