Oct 19 Exit Slip Grades/Competition Reflections

Today’s class primarily focused on two parts: questioning the accuracy of grades and a debate on competition/cooperation. Both are based on some thoughts made by Alfie Kohn, who is quite an extreme individual. This is a unique trait of his and it was interesting to see someone very fervent in these topics to express them out boldly. To begin with whether grades are accurate or not, I think it’s impossible to completely evaluate a student’s learning based on external assessments. Only the individual would know whether they know something or not once prompted with a question. I think grades give a general idea of how well students are doing, but there are so many other factors that should be taken into account that aren’t present within a numbered percentage. One can say someone who got 100% on an exam generally understands and mastered the concepts better than someone who scored 70%. However, what about two students who scored 70% vs. 71%, is the 71% student necessarily a bit more mastered than the 70% student? Sometimes there will be students who don't try and others who just have complications in life that hinder them from studying well. What were those 30% gaps that were missing? So we began to discuss proficiency scales, which is something I’ve never seen used in math growing up (it looks like a rubric for essays and presentations for English/social studies classes). Proficiency scales are helpful in that they can help identify areas students know and where they can work on. I think it’s quite interesting to implement in Alberta. I hear that this is used in junior high grades (7-9) in this province, and in high school they start using percentages (maybe along with proficiency scales). This method might be good since it allows students at younger ages to focus less on grades and more on improvement and developing skills to master them. Once high school hits, those who do plan on advancing onwards to post secondary may need some percentages for applications. Allowing them to also know their strengths and weaknesses in certain concepts will help them continue to develop good studying habits and metacognitive skills. Now, regarding Alfie Kohn’s comments on the negatives of competition, he has some good and true points, but are very generalized. Some people may find competition as a huge motivating factor to improve themselves in this world and how they can better themselves after seeing the improvement of other people. Cooperation helps build team/net work skills and allows one to figure out how to work with someone they don’t necessarily prefer to work with. This in turn can cause strife amongst the team and individuals blaming each other (lose-lose situation). But it's nice to weigh the pros and cons of each type and see where they can be implemented.

Oct 19 Inquiry Project start up

1. Define your question 

Search Topic: The Usage of Proofs in Math to Aid Student Learning 

2. Analyze your topic into concepts 

Concept A: The importance and value of having proofs 

Concept B: In which areas should proofs be implemented and how much rigor is necessary? 

Concept C: Different forms of proofs and their convincingness to students across stages 

When discussing the usage of proofs integrated in math, I want to draw upon existing educational theories, practices, and expert opinions. The role of proofs in math education stems from different philosophies on the purpose of education in mathematical understanding and the skills students need to succeed in the modern world. Including proofs can enhance students' logical reasoning skills and deepen their comprehension of mathematical concepts, while a lack of them might make the content more friendly/accessible but less water-tight/convincing. I happened to be exposed to multiple forms of proof in post-secondary. These may be utilized in teachings to allow students to not only get the right answer from a formula but also understand the inherent logic/structure that governs the notion. Without certain forms of proof, harder topics may be less intuitive. Allowing students to see different ways certain concepts came to be and how they are derived resonates with students in varying ways. The efficacy of a particular method often depends on the specific concept being addressed and the individual student's learning style. I was interested in proofs in latter years of high school. A lot of the equations are derivable based on previous knowledge students have encountered. This allows a build up of past ideas (or use them as a scaffold) into new ones. Certain definitions and evaluations were plopped onto the formula sheet, making it tedious for students to use them as they just take them for granted. Other students may feel indifferent but they lose out on some richness and value in linking information. Finding the sweet spot is hard and to balance how much time is spent on proofs in the classroom is something I have yet to experience.

Oct 19 Entrance Slip Reflection on marks, grades and their effects in schooling

I think grades and percentages are helpful for students in monitoring their progress to an extent. As a teacher it is very easy to assign percentage grades to assignments since it gives a ranking. Generally, grades can help indicate how well a student understands the course material. A high grade might suggest that a student has grasped core concepts, while a low grade might indicate confusion or gaps in knowledge. Sometimes, grades also factor in a student's participation, effort, or engagement with the material (though this might not directly reflect a student's mastery of the content). For my math classes back in grade school, every single summative assessment was a quiz/exam. This leads to little room for further improvement, if say, for mastering the concept or achieving a higher grade to apply for college/post-secondary. Indeed Kohn’s concern on the fact that the mainstream grading system needs revamping (since it raises negative effects on the desire to learn) is very evident in the classrooms I’ve been in. I think many of my classmates (myself included) were motivated to study/grind in order to get a higher grade, not necessarily to understand what was really happening. A lot of concepts were memorized or understood at an adequate level at the time, and then they disappeared after the exams. Going back to grades creating a ranking system or a social hierarchy, students labeled as "A" students are treated differently than those who typically earn lower grades. This labeling can affect self-esteem, peer relationships, and even teacher expectations. It also generates a lot of stress on students as they have to worry about their marks for tests. From the article, even high achieving students like Lucy are nervous about tests. Low achieving students may feel like they’re static and can’t improve, while high achieving ones will be pressured to remain at the top levels. All in all it creates bragging rights for the school so more parents can send their children there in order to get more funding. Grades are a conspicuous factor that students use to determine their success. But success for them need not to be expressed solely with a letter/percentage. The teacher may provide other projects/activities to evaluate a student, such as an creative math-art piece, a recorded mini lesson going over a problem, or presenting to the class. As long as they’re putting in effective effort in their learning with a positive attitude, the confidence levels should rise. I haven't experienced any course where a grade wasn’t present. Having categories like emerging, developing, proficient, and extending with goals/guidelines will help students find out which areas they should improve on. Although some students want grades due to competition, that notion of competing against oneself to do better in the future is just as effective. So for example assessments without grades like portfolios, socratic discussions, and class presentations can reflect the learning process. In a system without grades, the emphasis shifts from performance to learning orientation. It's also important for both the teacher and student to commit to whatever alternative assessment method is chosen. Parents and administrators also need to understand/support these alternative methods for them to be effective.