Mental Math with Numbers
Many
students don’t like math because they believe it has to do with defined
formulas and right and wrong answers; however, there are so many ways we can
manipulate the numbers that still fulfill the expectations. Math can be seen as
either ‘right’ or ‘wrong’, therefore it can be intimidating for students to
feel comfortable participating in math discussions as some may be fearful that
they will answer the question incorrectly. Teaching our students that we are
assessing and valuing the process of their thinking is so important to
teach and reaffirm in our math classes! There are many ways in which students
can get to the correct answer – and it is not a linear process! Each student
learns differently; therefore, no one way should be seen as correct or ‘better’
depending on the context. Each student may apply their own strategy – as long
as students are able to defend their reasoning, then they are gaining something
valuable from their mathematical experience.
Mathematical Reasoning
This is a
very important concept to recognize and implement within the math classroom. Jo
Boaler discusses the values in mathematical reasoning – math is so much more
than being an individual, isolated task; rather, it is part of a larger
community. Having valuable math discussions, debates, partner discussion, peer
collaboration, as well as teacher led lessons, student led lessons and of
course individual work. Including rich tasks (such as open-ended questions,
minds on, puzzles etc.) are a great way to allow students of all abilities to
participate and gain confidence in math. By encouraging multiple thinking
processes and allowing students to defend their reasoning (having no definitive
answer but rather, multiple correct responses). A study discussed in the following
video is very interesting – it concluded that students who worked together to
study and learn math were much more successful than those who studied and
learned math individually. Student-centered learning and discussion-based
lessons in math can be very beneficial to the ways we teach math.
In my placement, I often
encouraged turn and talk questions using whiteboards, as well as small group
activities to discuss math problems and concepts. Additionally, we would have many
beneficial conversations as a class when learning new concepts. Our
instructional coach facilitated a really meaningful conversation with my
students during a lesson about metric conversion relationships. She encouraged
my students to turn and face one another when talking, and if they were confused,
she insisted that they ask their peer directly for rephrasing or clarification.
Instead of the teacher facilitating a traditional lesson, it became a much more
collaborative, student-led, genuine conversation. Students felt comfortable to
share their ideas and make mistakes because she ensured that the classroom
climate was not judgemental or critical. Another strategy we used when teaching
students new concepts in math was something called a “community circle.”
Students would move their chairs into a circle around the whiteboard and have
no materials or distractions with them. We would then go over any questions
that students had on the spot, encourage discussion and have students come up
to the board to share their thinking. Afterwards, we had students write in
their math workbooks about something important they took away from that
community discussion.
Helping
students to develop and refine their mathematical reasoning skills is so
important in today’s society. In a world where technology is becoming so
advanced, there are so many career opportunities for our students if they are
able to problem-solve and develop multiple reasoning strategies. Companies like
Google and Facebook encourage their employees to talk through new ideas and
processes. Collaboration and discussion are the most important components
within the rich task; therefore, giving our students opportunities to share,
defend and teach one another about their ideas and findings will be so beneficial
to help develop their math brains!
This video discusses why developing reasoning skills are important in mathematics and in life!
This video discusses why developing reasoning skills are important in mathematics and in life!
Check out this link to learn more about what a rich task is
and how to go about creating them in the classroom!
This week I am reflecting on the importance of recognizing and reinforcing my students' abilities to use, communicate and share their thinking process. It takes a lot of confidence for a child to put up their hand in class and share their strategies – this should ALWAYS be rewarded with positive reinforcement. I never try to shut down my students' ideas because I know how much confidence it took to put themselves in such a vulnerable place. Calling out a child or claiming that their thinking is wrong may do damage to their desire to share in math ever again (I know it did for me!) Therefore, going forward I plan to create a classroom that really encourages and supports this kind of thinking so all of my students have the opportunity to grow their reasoning skills.
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