John Mason on questioning in math class

John Mason on questioning in math class 

I found Mason’s ideas interesting and applicable to inquiry-based learning. In particular, I think they provide useful insights in conducting p4c-style method of teaching that I’m especially interested in. The role of the facilitator in community of inquiry is to help the learners to ask themselves questions that lead them to the solution to the problem, rather to lead them to solutions by asking them questions that lead to answer. I found the distinction between “asking as telling” and “asking as asking” which is based on the distinction between “listening-for an expected response and listening-to what students are saying (and watching what students are doing)(p. 515)” insightful. This idea can help the facilitator in community of inquiry to find ways to engage the learners in such a manner that they lead to ask useful questions and in the course of answering those questions learn the subject that they are supposed to learn. Another interesting idea discussed in Mason’s paper is asking students “to construct examples of mathematical objects meeting various constraints. By carefully choosing the constraints so as to force students to think beyond the first (usually rather simple) example that comes to mind”(p. 516). I will try to come up with ways to use the method of formulating questions by students and constructing examples when I plan my lesson for the long practicum.

 

Reflection on micro teaching:

Based on self-reflection and the feedback, I think there purpose of our activity wasn’t clear and made students a bit confusing. We also could have allocated more time for the activity and engaging students in learning so that they could have had enough time to express their ideas and solution methods.

Lesson Plan for Micro Teaching

Shan, Amandeep, and Pari

Subject: Probability of independent event                      Lesson Number: 1 of 1

Grade: Grade 8                                                         Time: 15 minutes

Big Idea for the Lesson: Finding probability of independent event.  

PLOs:   Student would be able to learn about the following topics:

• Data Analysis - critique ways in which data is presented
• Chance and Uncertainty –To solve problems involving the probability of independent events    

Objectives:   Students are expected to learn about how to find the probability of an event by using the definition of probability.     

Materials: paper, pencils, and laptops or tablets.

Hook: (about 1 min)

Showing the 1-die situation using MIT Scratch

Introducing the pattern that all numbers increased together.

Development: (about 13 min)

·      Teacher-led: (about min 4)

*Demonstrate sample space, outcome, event, probability, experiment, and trial. (2min)

             Demonstrate the MIT Scratch simulation and the EXCEL simulation (2 min)

·      Class activity: (about 9 min)

* Inviting students to explore the 2-die situation and share their solutions. (4 min)

             

  More questions: (5 min)

  Toss a coin, toss two coins, and 3-die situation and their sample space.

Assessment: Students would be assessed on their participation and work throughout the lesson (Fist of five).

Closing: (about 1 min): Students would be advised to write down key points of the lesson on their notebook.

2 Column Solutions

Right Angles:
Given the number of sides of a polygon, what is the maximum number of
right angles it can have? (p.173)

Exit slip: Hewitt’s video reflection

The video we watched during the class showed me an interesting way of teaching math: a balance between the teacher-centered approach and the student-centered approach. By asking questions Hewitt engaged all students in learning math and by asking the whole class to answer at the same time made the class active and enjoyable. This way also allows the teachers to assess their students’ understanding as well. Long wait times and repetition help the teachers to make sure all students are on the same page.  

 

Arbitrary vs. necessary in the math curriculum

According to Hewitt, something is arbitrary “if someone could only come to know it to be true by being informed of it by some external means” such as books and teachers. That is, there is no further reason about why it is the way it is, thus anyone who wants to know it needs to be informed by external means. Arbitrary cases include, for example, naming conventions (calling squares, “square” or using Hindu-Arabic numerals for numbers). The arbitrary conventions are based on choices which have been made at some time in the past and they could have been different. In contrast, “the necessary is dependent upon the awareness students already have”. That is, the student should be able to work it out without the need to be further informed.

For a particular lesson, I will see if students do have the required awareness for the subject I am supposed to teach. If so, I will consider it necessary and introduce tasks that help students to use their awareness to work it out. Otherwise, I will consider it as arbitrary and explain the rules or terms.

Knowing what is necessary and what is arbitrary helps me make math more enjoyable for students.  Helping students to use their awareness to work out the math problems would let the student enjoy doing math (that is the most interesting part of learning math) and would not see math as a boring subject consists of numerous formula that need to be memorized.

Exit slip: SNAP math fair

I was impressed by the students’ presentations. They worked together and took turns in presenting their math puzzles to us. I really liked the stories behind the puzzles and the way that students related their puzzles to the artifacts in the museum. It made their puzzles more interesting and engaging.

I’ve also found it interesting to put students in the position of teaching and helping others to solve the problems as the best way to understand a concept/problem is to explain it to someone else; teaching is the best way of learning.