Trigonometry Group learning Activity (Week 11 Reflection)

In class this week, I lead a learning activity for a grade 11 University level mathematics class, for a unit in Trigonometry that involved Trigonometric ratios, and the Sine and Cosine Laws. The students were arranged into groups of 2-3 since we have a smaller class size, however with a regular class size, it would be best to have larger groups of 3-4 students. The instructions of the activity were explained to the class verbally, and the written instructions were displayed on the board to accommodate all students. In this activity, the students were given a worksheet and were asked to work together to solve the 4 questions provided. This activity also involved a word scramble, where the students were able to unlock some of the letters to the mystery word after answering each question on their worksheet correctly. In addition, each group was given a HELP card, where they had the option to call on another member from a different group for assistance if they were struggling with a question. The HELP card could only be used once, and it was added into the activity to limit teacher intervention and encourage the students to work together. The last question on the worksheet was a word problem that was to be written on chart paper and presented to the class. Each group received a different word problem on their handout, and their presentation needed to include a diagram, calculations, and their mathematical thought process. In a real class setting, after completing the activity, the students can be given the opportunity to walk around to view each groups work on the word problems, copy them down into their notes, and make sure they have a good understand of how to solve each problem.

First page of the worksheet

Some of the key points in this activity are that it is important to strategically place students into groups, ensuring that each group consists of students with a range of abilities. This will create a positive learning environment, and encourage peer tutoring and collaboration. This activity caters to both instrumental and relational understanding and it is best utilized as a review, after the students have learned these concepts in class. Thus, the teacher should refrain from quickly assisting the students, and wait until they have used their HELP card (assistance from another group) before stepping in to assist struggling students. The teacher should also be circulating the room to ensure the students are on track, working together, and that everyone is participating in the activity. Additionally, it would be beneficial for the teacher to keep anecdotal records or to use a checklist to track student progress. Another important note is that the teacher should ensure that the students have enough time to work through the worksheet before presenting their problem to the class. Lastly, the word scramble portion of the activity promotes literacy, and it was a great way to get the students interested and keep them on track, since they wanted to keep unlocking letters to solve the final puzzle.

This activity can also be structured as a competition, however the teacher should make that decision based on the students maturity level. It is important to ensure that the students aren’t rushing to win, and that they are all participating and learning through the activity. Another option would be to give each group a prize after everyone has answered all four activity questions and completed the word scramble. In this way, everyone will be able to enjoy a reward!

                                           

                                     Above is the second page of the worksheet for each group

Group Learning through Activities in the Classroom (Week 10 Reflection)

In class this week, we participated in a learning activity for a grade 10 applied mathematics class, involving linear systems. The technological tool, Visual Basic, was used to demonstrate graphing the linear equation y = mx + b and the changes in the slope and y-intercept were explored. After the review of linear equations, we were divided into groups in a way that would be very fun and engaging for students. Each student randomly selected a paper with a letter on it, and was asked to call out a food that starts with the letter they were given. The groups were then created by grouping the students who called out foods starting with the same letter. A simple exercise like this is a great opportunity to get the students interested and excited before participating in the activity.

In the group activity, each student was assigned a word problem that involved the process of first figuring out the linear system, and then using either substitution or elimination to solve for the unknown variables. This was a great activity because each group member had to work together and write their final answer on a chart paper, that was later presented to the class. Collaborative learning is very beneficial for all students because they learn how to work with others, obtain knowledge from their peers, and they are able to help those who are having difficulty. Group work often allows students to feel more comfortable and less anxious when working on a problem they do not fully understand, which creates an effective and positive classroom environment.  

A solution to a group's assigned word problem

After completing the activity and sharing the results with our peers, it was interesting to discover that everyone used the substitution method to solve for the unknown variables, opposed to elimination method. This was particularly interesting because the linear systems were simple enough that using elimination would have been easier and more efficient. Through discussion with the class, we came to the conclusion that we all chose to use substitution because we all felt more comfortable with it, since we were taught that method first as young students, and it was the most practiced method. It would be interesting to discover if we all would have used elimination if we were taught that method first in school.

Another solution a group's assigned word problem

Another activity that we did in class involved conceptualizing and representing linear relationships. In pairs, we had to analyze the given dot pattern and find the general formula to predict the number of dots at any given minute of the sequence. The purpose of this activity was to see how people visualize the sequence of dots differently, and it was interesting to hear everyone’s thought process once we presented our ideas on a chart paper. In pairs, we came up with various ideas to explain the sequence. Some students visualized the sequence in stages, while others imagined the sequence changing all in one step. Some examples used to describe the sequence were Bacteria growth, Cell division, and 1 petal being added to each stem like a growing flower. It is very important to encourage students to conceptualize math problems in different ways because it allows students to think more abstractly, and view questions from different perspectives.

The photos above are from the conceptualizing and representing dots problem

Positive Attitude and Approach toward teaching Secondary Mathematics (Week 9 Reflection)

The article “Adolescent Learning and Secondary Mathematics” stressed that an important part of teaching is creating a positive and engaging classroom environment for students. According to the article, this can be done by introducing more group work, giving attention to students’ ideas and interests, and using their social world to produce more engaged learners. I agree with these ideas as a means to increase engagement because I had success using similar techniques in the grade 11 Math class I was teaching during my first practicum.  I found it very beneficial to get to know the students, and incorporate their personal interests into the lessons I was teaching, as well as their homework questions. Simply integrating the students’ names into the word problems and creating math questions around their favourite sport or TV show really captured their interest in learning mathematics. Not only did I notice an improvement in their engagement and participation in my class, but in addition the students appeared to be in a good mood, resulting in a positive classroom environment. It was amazing to see what a positive impact showing the students you care has on their whole attitude toward learning.

Another key point that the article addresses is cognitive bullying, which describes the kind of teaching that ignores or negates the way a student thinks, imposes unnatural thought processes, undermines the students’ effort, and causes stress. These actions are reoccurring over time. Ultimately, cognitive bullying contributes to generating fear and anxiety over certain mathematical concepts due to the students’ negative experiences in the classroom, and this negatively impacts their learning. As a student, I was fortunate enough to have teachers who were very open to using a variety of methods to solve mathematical problems, and they did not force students to only approach a problem the way it was being taught. I recall using different methods than my teachers on a number of occasions and asking them if my methods were acceptable. After checking my work, my teachers approved the techniques I used and provided positive feedback and encouragement for trying something new, as oppose to disregarding my work and telling me to do it “their way”. As a result of these positive experiences, I was able to grow as a learner and I was inspired to explore many methods of solving different math problems.

 As a teacher, it is very important to get to know your students and structure your lessons around their learning needs. Students in your classroom will not all learn the same way; therefore differentiated instruction is very important. Teachers must have patients and work on building students self-esteem when teaching mathematics, especially with the weaker students. Sometimes knowing that someone believes in you, and wants you to succeed is all the motivation needed in order for a student to be in the right mind frame and willing to learn math. According to the article, an effective way to build the students confidence is by starting a task with something they know fairly well, and continuously building off of that to teach a new concept. This approach recognizes learners’ existing knowledge, and offers the opportunity to add more information to their preexisting knowledge base. By building up the learners’ self-esteem first, it is more likely that they will be open to learning the new material and feel empowered to succeed.