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 21st 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 21st 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 21st 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
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