group summary of the interview

(1) Why do you think we learn math in school, and why do you think math is an important or unimportant subject?
The general consensus is that Math is important to understand the world around us, and is a critical prerequisite to learning essential skills such as statistics, accounting, physics, poetry, etc. Additionally Math helps to develop critical thinking and problem solving skills.

(2a) For students: When learning a new material, do you tend to memorize the steps in solving a problem or do you try to understand the meaning and idea under each steps? and why do you do so?
Our students, who both struggled with Math, had differing opinions on Instrumental versus Relational understanding. The first student, who learned using a "work at your own pace" system, believed that the best method for him was 100% instrumental learning, since he viewed mathematics as an unnecessary learning exercise, and had no interest beyond passing the course. Our second student believed that if he had an Relational understanding, that it would be easier for him to develop (or "memorize") the Instrumental understanding.

(2b) For teachers: When teaching a new material, do you just work through a problem and showing all the steps in solving a problem or do you explain or try to explain the idea in each of the steps involved in solving a problem? and why do you do so?
Two of our teachers believe strongly that Relational teaching leads to a stronger understanding of the material than Instrumental teaching, which in turn allows the students to better apply their knowledge to a wider variety of problems. Our third teacher believes it is important to emphasize a variety of teaching techniques, both Relational and Instrumental, combined with classroom discussion and a final summary of the Relational concepts.

(3) What do you think of TPS (Think-Pair-Share) techniques where students break into groups of 2 to discuss the material before the class discusses it as a whole? How about groups of 5 students?
Two of our three teachers were willing to comment on TPS techniques, but for different reasons. Our first teacher believes that TPS can help both as a classroom management tool, as well as help reduce the possibility of public humiliation that occurs when a student answers a question wrong. Our second teacher supports TPS techniques because the students take a more active roll in their learning. She finds it inspires creativity in the students, improves their ability to communicate using math terms, and strengthens their understanding of the concepts.Both students believe TPS techniques would help with classroom management. One student expressed concern regarding groups of 5, where not everyone may be actively involved.

(4) Administering tests can be an effective tool in determining class proficiency before moving on to new material. How frequently do you believe tests should be administered?
Our teachers as a whole believed that constant assessment is necessary, but did not believe that tests were essential to administer frequently. They all stressed that alternate methods of assessment were just as effective. Both students explicitly stated that tests should be administered at the end of every unit, and suggested one test a week as a good pace. One of the students specified that he prefers tests to homework assignments as a means of assessment.

(5) What are your views on traditional class lecturing versus a system where students could work at their own pace and each individual could spend extra time on material they found difficult?
Our teachers agreed that a "work at your own pace" system would be nice, but is very difficult to implement due to time constraints and class management. Although not included in the written response, the one teacher, Mr. Jack French, did mention in a phone conversation that the administration and parents pushed heavily against this system due to students having to take a Grade 12 math block to finish their required Grade 11 mathematics, which by the program requirement, they eventually passed with 80% or better. One student expressed concern that a "work at your own pace" system would result in the students getting behind, while the other student was concerned about teacher unavailability.