Online Class - Video and Webinar Reflections

            The videos and webinars that I watched for the online class this week were very interesting and stimulated a lot of thought for me as not only a future Mathematics teacher, but also as someone who genuinely enjoys math in general! I put a lot of thought and effort into choosing which videos I wanted to explore further; first, I specified the list to a few that look captivating to me, based on their name and topic. Then, I narrowed this selection down even more by reading the descriptions – if they were provided – for each of these videos in greater detail. Finally, I was able to select 4 videos/webinars to view, totaling about 100 minutes, collectively.

The first video that I watched, and the longest, was called Implementing Effective Mathematics Teaching Practices by Peg Smith, which she presented as the opening keynote at the 2015 CMP Users’ Conference. The University of Pittsburg professor uses “Connected Mathematics” as an example to describe the eight practices from the NCTM Principle to Actions and how they impact student learning. Primarily, Peg uses NCTM’s book as a framework for her discussion on how to effectively teach Mathematics. These practices explain to Mathematics teachers how they should work in the classroom, and how to anticipate and monitor the solutions being pondered by students. In this keynote lecture, Smith depicts the following practices (as taken from NCTM, 2014): establish mathematics goals to focus learning; implement tasks that promote reasoning and problem-solving; use and connect mathematical representations; facilitate meaningful mathematical discourse; pose purposeful questions; build procedural fluency from conceptual understanding; support productive struggle in learning mathematics; and elicit and use evidence of student thinking (NCTM, 2014). Peg opens by having the audience deconstruct and analyze a case study and transcript, then they discuss the practices, followed by a conclusion. She states that these practices are the vehicle that can essentially bring the math curriculum to life. Establishing goals is at the core of instruction, that ensures all students learn the expected outcomes. I have learned through my undergraduate years at Brock University the importance of starting with the curriculum, in any subject matter. Peg emphasizes the importance of this as the difference that causes students to learn. “Connected Mathematics” (CMP) is a strategy that I will use in my own future endeavors as a Mathematics teacher. CMP is a problem-centered curriculum approach promoting an inquiry-based teaching-learning classroom environment. Mathematical ideas are identified and embedded in a sequenced set of tasks and explored in depth to allow students to develop rich mathematical understandings and meaningful skills. This is a great way for me to help my students develop their mathematical knowledge, understanding, and skill along with an awareness of and appreciation for the rich connections among mathematical strands and between mathematics and other disciplines. I believe that all students should be able to reason and communicate proficiently in mathematics, and this approach will encourage the knowledge and skills necessary to do so. I found the video that Peg showed (Ms. Rossin’s class) to be especially helpful. The teacher in the video did not tell or show the students what to do; rather, she posed purposeful questions to get them focused and orchestrate productive discussion. As Peg engages the audience in CMP, guided by the eight principles listed, they can replicate students and act as learners in the activities presented. Professional development opportunities like this are ones that all teachers should be striving to attend, since our career entails frequent and ongoing professional growth in order to be the best that we can be.

The next video that I decided to watch was Dan Finkel’s Five Principles of Extraordinary Math Teaching TED Talk, via TEDxRainier in 2016. Finkel invites viewers to approach learning and teaching Mathematics with courage, curiosity, and enjoyment by focusing on the motivation, history, aesthetics, and deep structure of mathematics. He challenges the popular belief that math is dull, meaningless, and disengages students. As a young educator, I genuinely believe that making learning fun and enjoyable should be the main aim of every teacher. Learners are only fully engaged and motivated when they are interested in the topic and have a sense of enjoyment in it. The first principle “ask an authentic and compelling question” invites students to strive for a satisfying solution, since humans are inherently curious. The second principle, which acknowledges that we need time to struggle, helps us become “tenacious, courageous, and persevering”. Giving students time to think and grapple with real problems encourages them to interact, share perspectives, and deepen their ability to take risks and conjecture. The principle stating that the “teacher is not the answer key” addresses the fact that you, as the teacher, do not need to know everything. In this regard, teachers – and other adults – can teach children that learning is not failure, and encourages us to cooperate with the students to solve the question collectively. It also fosters cooperation between classmates via mathematical conversation and debate. The fourth principle is saying “yes” to students’ ideas, which I think can be difficult at times. Finkel says that there is a difference between correcting students when they’re wrong and saying “yes”. In other words, educators must accept children’s ideas and value them, and allow peers to show them why they may be wrong. The final principle explained is playing, which involves exploring, fighting, breaking things, etc. playing with math gives students ownership and gets their creative juices flowing. These 5 principles are crucial for me to implement in my future teaching practices, and I will ensure that I practice them each and every day in the classroom.

A third video that I found rather invigorating was How Professionals Use Mathematics to Solve Real-World Problems in the 21^st Century – a webinar by Keith Devlin. The speaker commences by presenting an article claiming that all the mathematics one learns becomes obsolete later in their lifetime. He continues to acknowledge that the way mathematics happened in the past is very different from how it is done now. He then addresses the question that stumps many humans today: Does having new mathematical tools mean we no longer need to teach calculation? Of course, he explains why the answer to this question is “no”. however, he claims that we no longer need to teach for accurate or fast execution. Instead, we must teach for understanding. As a teacher, I must understand that today’s users of mathematics require different skills. A creative analogy that he makes is that yesterday’s mathematics users had to learn to play many “instruments”; today’s mathematics users, however, have to be able to conduct an orchestra. Some of the things that we must teach our students, then, include number sense, deductive reasoning, creative problem-solving, and more. Therefore, we must teaching thinking! A heuristic is any approach to problem-solving, learning, or discovery that employs a practical method not guaranteed to be optimal or perfect, but sufficient for the immediate goals. In mathematics, educators need to develop their students’ post-rigorous thinking by practicing algorithms and procedures optimized for efficient performance. It is only through teaching for effective understanding in the 21^st century, then, that mathematics can be made meaningful for our students and allow them to develop their mathematical thinking skills.

The final clip that I wanted to reflect upon was another TED Talk (from TEDxNorrkoping) called The power of believing that you can improve by Carol Dweck. As soon as I read “growth mindset”, I knew this would be a video of grate interest and value to me. I have always seen myself as someone with a positive, optimistic viewpoint on life, and I try to facilitate this same perspective for others. The idea that we can grow our brain’s capacity to learn and solve problems fascinates me as not only a person, but also as an academic and future teacher. Dweck uses this talk to describe two ways to think about a problem that’s slightly too difficult for you to solve: either you believe you are not smart enough to solve it, or you just have not solved it yet. It is a major goal of mine to teach students to adopt the latter of these two mindsets. Having a positive self-conception is a critical life skill for humans to possess, which we can use to structure ourselves and guide our behaviour. I aspire to motivate students and enhance their self-regulation, and their impact on achievement and interpersonal processes. Instead of running from difficulty, cheating, and having a fixed mindset – like the students on the left side of Dweck’s opening example – I wish to raise children to think “yet” instead of thinking “now”. achievement is meaningless if we cannot better our efforts and become more knowledgeable and skillful. In contrast, if someone recognizes that they can be better and make every effort for this, the point at which they are starting is irrelevant, since they will eventually reach and exceed their goals for success. This is illustrated in the second example, where the Native kids outdid the Microsoft kids because the meaning of effort and difficulty was transformed so that the kids’ neurons made stronger connections, making them smarter. I believe that this should be a primary goal for all educators, since understanding that abilities are capable of growth is all one needs in life to succeed.

References

Devlin, K. (2018). How Professionals Use Mathematics to Solve Real-World Problems in the 21^st Century. Confent Video. Retrieved from: https://vimeo.com/292393546

Dweck, C. The power of believing that you can improve. TEDxNorrkoping. Retrieved from: https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve?language=en&utm_campaign=tedspread&utm_medium=referral&utm_source=tedcomshare

Finkel, D. (2016). Five Principles of Extraordinary Math Teaching. TEDxRainier. Retrieved from: https://www.youtube.com/watch?v=ytVneQUA5-c&feature=youtu.be

National Council of Teachers of Mathematics (NCTM). (2014). Principles to Actions: Ensuring Mathematical Success for All.

Smith, P. (2015). Implementing Effective Mathematics Teaching Practices. CMP Users’ Conference. Retrieved from: https://www.bigmarker.com/GlobalMathDept/Implementing-Effective-Mathematics-Teaching-Practices

My Weekly Report and Reflection 10 (Week 18)

Holy, it is hard to believe that this is my final blog of the year for this course! It has been ana amazing experience and I have loved every second of my time in the “Teaching Mathematics (Part 1)” course. This week, it was my turn to lead a learning activity. I really enjoyed the entire process: creating this activity and facilitating the students’ engagement in it!

This project provided me with several crucial insights as a future Mathematics teacher. I organized this activity based on there being three students per group. In a full class, I would put the students into three or full smaller groups. They would complete the main activity in a “Jigsaw” style. They would start by discussing the examples that they are given with their small-group members for about 10-15 minutes. Once all groups have finished considering their respective examples, each group member will be dispersed into a new group with one person from each other group. Here, they will represent their former, original group by speaking as an “expert member” and explaining their problems with their peers. Finally, the class will engage in a class wide discussion involving everyone, where we will converse some RUBRIC writing that we did throughout the process. This will include times when we were “STUCK”, special findings or “AHA!” moments, times when they reasoned or wrote “CHECK”, and other key ideas/moments/learning experiences as they “REFLECT”.

Kirsten said it could be good to add to each example by extending them so that they fit in more than one category. Thus, I began asking groups to turn these rather “black-and-white” examples into ones with multiple solutions by adding “grey” areas. For instance, in a question that involves a cigarette company asking 5 people in Niagara if they smoke obviously illustrates misleading statistics through small sample size. However, I could prompt the students to alter this question by adding, for example, that the cigarette company asked 5 people “Do you smoke cigarettes, even though they are disgusting and likely to kill you?” This would make the question not only a small sample size, but also faulty polling, since they are clearly persuading the respondents to answer that they do not smoke.

We also debated making this activity technological (done on computers), but concluded that we believe the hands-on format is more fun, engaging, and better suited for Grade 12 College level students. Although there is a time and place for technology to be implemented in learning, that place in not this particular context. High-achieving and Gifted students may benefit from answering the activity example questions online and independently. However, College level students prefer (for the most part) hands-on and visual-kinesthetic learning. Hence, I would leave this activity as is when teaching it in the future to a College or Applied level class.

Another thing that I started doing with the second group that worked really well was having them debate their answers to each example and try to get their group mates to side with them and change answers. This encourages the students to use higher-order thinking skills and consider other perspectives. It also enhances students’ verbal and communication abilities, which is a life skill necessary for all college-bound students. I find that this strategy worked especially well when the example actually did have more than one answer possible, since no students were “incorrect”. For example, the example that posed the student as the head of a marketing campaign that wants children to wear Champion brand clothing had more than one potential “correct” answer. The example went on to state that “you phone 8 of your friend’s kids, 7 of whom have admitted to wearing Champion”. After pondering this question, it is evident that it could have more than one possible solution: small sample size and selective bias. More open-ended questions like these encourage higher-order thinking skills and make the discussion was much livelier and more meaningful!

Overall, this curriculum assignment was a terrific learning experience! Not only was it a great opportunity to lead my peers through and activity and discussion, but it was also my first structured opportunity to teach a math lesson of any type in the classroom. Since Mathematics is my second teachable, I have never actually taught a structured classroom lesson in the subject, and this is something that I am somewhat anxious about doing in my future placemats. It is imperative, then, that I am provided with such opportunities to practice and receive feedback on my teaching and instruction. Experiences like this one are crucial starting points and allow me to exercise my “Teaching Intermediate/Senior Mathematics” pedagogies and practices in practical and applicable ways!