Power of Yet

I did not know the importance of the growth mindset until the first day of classes, when all our classes addressed this concept. This is a powerful mindset to have, but in my opinion it takes time to get used to this type of thinking. This style of thinking is not only for teachers and educators to inculcate into their daily lives but to also teach children this powerful way of thinking. It requires one to re-wire their brain to always think with a positive lens, no matter what the outcome may be. It is to teach students to stay motivated despite their failures and to keep persevering until they get the answer. This is something I have observed being taught to the students daily; when they are frustrated and they feel like they want to give up, the teachers have taught them, “The Power of Yet.” Students are taught not to say, “I do not get it,” but rather, “I do not get it YET.” This teaches students not to give-up, that struggling is a way of learning and when they do get the answer they will remember it, compared to when they get the answer right away. It is also important to keep students motivated with not only the attitude they have towards math but also as they work through the math.

One way to keep students motivated through their work is to design the math problems in a way that intrigues young minds to keep working until they reach a solution. As educators it is our duty to provide students with multiple ways of representing their work. It is also important that math questions are designed to allow students at all levels get started working through the problem.  Here is a list of what makes a good math problem:

• Relevant: It is important to pose question to students that they can relate to
• Wide base: The problem is set-up and is doable by a wide range of learners
•  Initial success: They offer initial success, motivating the learner to push beyond their limits
• Low threshold and High ceiling: it has an opportunity for students of different levels of challenge to be able to tackle the problem, but also the potential for learners who like the extra challenge to extend the problem
•  Engaging: The questions are set-up to engage the learner and draw them into solving the problem
• More than one way: The problems have more than one way of arriving at the solution; thus sharing these different ways allows students to deepen and broaden their thinkin

Another aspect to consider when looking for a good mathematical problem is to think about the mathematical processes that will be taking place as the students work on the problems such as:

•   Problem solving: Structured to include an inquiry problem where students have to investigated to figure out the solution, by making connections to previous concepts and making new discoveries.
•   Connecting: previous experiences in problem solving help in my making new connections to new mathematical concepts
• Reasoning and proving: As students develop new ideas and concepts they also develop reasoning and proving skills
•  Representing: Students can represent work using concrete materials, pictures, diagrams, words and numbers
•  Reflecting: Questions posed by peers and teachers are a good way of getting students reflecting on why they may have chosen a certain method to represent their solution, or why they think their solution works, etc.
• Communicating: Students are able to prove their solution visually, orally or through writing
• Selecting tools and computational strategies: Students are able to use a variety of tools and strategies to represent their answer

It was really important to know these seven mathematical process when observing students doing the problem-solving assignment. This was definitely my favourite assignment to observe students trying to solve math problems and how they used variety of mathematical process to find their solutions. One conclusion I would like to draw from the assignment is that the students I observed really took their time answering the questions. They also asked clarifying questions to make sure they were on the right track. I find that in the classroom sometimes there are students who may know the answer, but because they are too shy to ask, end up making mistakes on a test or assignment. As educators we must create a climate where students feel encouraged to ask questions to clear their doubts and fears and where enough time is allotted to deepen their mathematical concepts.

To conclude, this has been a very interesting class, I have learned a lot over the past twelve weeks and I continue to work on my growth mindset when working on creating my lesson plans. As I work to make them engaging and meaningful for the students at my placement. The work can get overwhelming at times, but having learned all the great techniques to make math subject students look forward to, and on way is the use of literature. I had the opportunity to use this technique and found that students were really captivated by the storytelling technique and I hope to use this and many other techniques learned in class this year!

Level-up

Estimating

We started this week’s class trying to figure out how many cookies in the cookie jar! This activity helped us to gather data for all the estimated values and were plotted onto a stem and leaf graph. I first started my guess with 126 cookies, and the way I reached this number is by counting the number of cookies on the bottom layer (18) and multiplying it by the number of layers (7). The more I looked at the cookie jar as it was being passed around the room; I felt the number was too high of an estimate. When I looked at the jar again I saw 4 layers instead of 7, giving a total estimate of 72 cookies. Now I felt the guess was too low, so I took an average of between 126 and 72 and came to a conclusion of 99 cookies. This was a better estimate since it was very close to the actually number of cookies, 105 in the jar. It was really interesting doing this task to show students the importance of estimating. We make estimates all the time, whether it is in cooking or trying to get ready in time to catch the bus.

How many cookies in the cookie Jar?
(Khalid, N © 2016) 

Graphing

We then took the data and plotted everyone’s estimates on a stem and leaf graph. Something interesting I learned is that two sets of data can be placed on the same graph side-by-side to compare and contrast the data. In one class most people guessed around 72 cookies, while in another class there were around 84 cookies as the estimate. It was nice to compare the data that was taken from other classes. We simply started out with guessing the number of cookies in the jar, which lead us to make many more discoveries. We learned much lessons on gathering data, such as graphing, finding the mean, median and mode and their significance. So many lessons can be taught using this simple activity, which I found very interesting.

Talking about the mean, we were also shown how to demonstrate to students what mean would look like. We learned it is the same as leveling and distributing the bars evenly. It was easy to show this using manipulatives such as blocks. Demonstrating to students that if something is distributed unfairly; how can we level the bars to show a fair representation of that distribution.

Uneven Distribution
(Khalid, N © 2016) 

Evenly Distributed (That's Mean!)
(Khalid, N © 2016)  

Using technology:

Another method of comparing and contrasting data was on a really interesting website called Tinkerplots. This software helps students visualize and model the data to show differences and relationships between various attributes. This software seems a little hard to work with due to all the complex features that it has, but with a growth mindset it should be easy to overcome it with a little practice. I feel that this is a cool tool to use in the classroom and students will enjoy being able to visualize the data.