Questioning in Mathematics Reading

Mason's ideas on questioning fit very well into an inquiry model. Inquiry is a student-led, challenge first/lecture later (if at all) style, and Mason's ideas about integrating difficult questions to lessons is directly tied to that. When we make questions rigorous for students, we teach students to not be afraid of getting stuck, and they learn to be more resilient to tough problems. If we model how to cope when a problem stumps you, we show we are empathetic (we also can be stumped!) and they can tackle problems on their own, without the constant guidance of a teacher, which inquiry requires.

In my unit planning, I want to make notes of specific questions I want to base my lessons around. I think by having a guiding question, lessons can have more of a natural flow to them, and the lesson will naturally become more inquiry based.

Lesson Plan for Micro Teaching: Linear Relations

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? How do you graph it?
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 graph paper whiteboard/markers
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: skeleton note sheet that they fill in at the end of the lesson Extensions: graphing negative slopes, or more complicated functions (individually on their own graph paper)
Lesson Plan - Teacher-led, Class/Group Activity (10 min) 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). Alison: 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. 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. 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: 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 min) 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, 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?

Two Column Math Problem Approach

 Hopefully these pictures are clear!

Dave Hewitt Video Reflection

Watching Hewitt teach was inspiring. His use of the space, of the students, of choral speaking - all of it worked together to make an engaging and thought-provoking lesson. I've been thinking a lot about questioning and thinking skills lately, and being mindful of the way we frame questions, especially in mathematical contexts, is crucial for student learning. The way Hewitt phrased his lesson on algebra as a "thinking of a number" question provoked the kind of curiosity and puzzle solving that I want to be able to foster. I definitely want to test out his teaching strategies, such as the choral speaking, the long wait times, the repetition, etc., in my classes on practicum.

Snap Math Fair Reflection

The SNAP Math Fair was a fantastic experience. The kids were so excited to show us the puzzles they had been working on and I was very excited to see them excited! It was a very comfortable environment, and I didn't feel like the students were nervous or under pressure, just very willing to help others solve their problem. I think this is directly the result of the clear guidelines of SNAP, and the fair definitely got me on board with its approach. I thought it was great to have the students recreate the problem to suit an exhibit of the choice, and show their project in that context. You could tell it really personalized the question for the students. I wish I could have seen all of them - the time was too short and the discussions too good!

Arbitrary and Necessary

The arbitrary part of mathematics is the language and definitions we use. It is the stuff we invent for the purposes of communication. For example, Hewitt says that we choose to write thirteen as "13," but there are other equally valid ways to write it if you wanted to. 13 is just the widely recognized and accepted form. Arbitrary means it is something that must be memorized in order to be known. Necessary mathematics, on the other hand, can be worked out independently. Students need to be aware enough of to accomplish it though. To decide if something is necessary or arbitrary, we have the think about whether or not you could figure it out yourself, or represent the exact same thing in a different way.
This article made me think about what questions I ask. Am I asking students to regurgitate a arbitrary fact, or am I asking them to work something out logically? When I think about that, then I can provide students with the appropriate question. Hewett's example was a teacher getting a student to "think about" the name of the number that occurs most often, when that question had no thinking involved - either the student remembered it or not.
I really want to implement a lot of inquiry based learning in my math classes, and I think focusing on the necessary questions, where students get to work things out themselves, is definitely my aim.

SNAP Math Fair

In my elementary school, I remember there being a science fair that would happen every year, and each year I would get excited about it - thinking about fun ideas of what I could do. But since the fair was always done outside of class time, I would always end up being busy with extracurriculars, like dance and theatre, as well as regular homework. I love the idea that the work for the SNAP Math Fair is done entirely in class and that everyone participates.

I also love that it isn't competitive. I was very intimidated by math contests as a kid and an adolescent, so I never participated, despite being a fairly strong math student. I think the Math Fair creates an alternate challenging opportunity for students, where, instead of everyone receiving the same questions and ranking themselves against their peers' scores, students work on different puzzling problems, and can teach each other. 

I would love to implement a SNAP Math Fair in my practicum high school, but I've already heard from my SAs how densely packed the curriculum content is. I am worried that I won't be able to afford the time required for students to work on their projects during class time. I will do my best to make it happen though, because I think it would be really rewarding for the students!