Math Games

Reflection 6

                In this week’s module in math class, I explored math and technology as a part of my online modules. I thought that this topic was very relevant because it is 21^st century and technology is all over the place! So, I thought to dedicate my blog today for math games.

Why Play Math Games?

                It does not matter what age you are at, you always want to play some sort of a game. Games are fun and motivating and it gives opportunities to explore and grow your minds. Math games can very accessible because you play them right from the comfort of your home. It can be affordable, might not cost too much, but it can also be expensive. Let us focus on math games in particular now, why play math games?

·         Playing games encourages strategic thinking

·         When you play a game repeatedly, you are supporting development of computational fluency

·         Games give ready-made practice and a teacher can assess while students working on the game

·         Students can build a deeper understanding of ideas

·         Games can also support a school-to-home connection

What is better than sending a student home who is very excited about learning math only because you introduced a game? Take prodigy for example, from personal experience, I have seen students spend a lot of time at home playing prodigy.

                                                                        

What is Next?

                You just sent some students home to play math games or they are playing in class; but now what? What would you do next? You definitely do not want to waste time. Yes it is awesome to get students excited because they are about to play a game and are having fun, but are they really learning? How can you find out? Reflections! Reflections are really important otherwise students would have just wasted an opportunity for learning.  

                I think it is really important that every students reflects on the mathematics involved in the game, the challenges that they faced, and the strategies that were used. So, as some strategic reflection questions, they can either be oral or written. Some good questions can include:

1.       What were the fun bits in your learning when you played the game?

2.       Write two things that were difficult in this game.

3.       What was the tricky part about the game?

4.       Can you connect the math you used in this game to something you already know?

Game Selection

                There are many math games out there, but how can you narrow down your list? Try to think about what you want the students to achieve. Do you want them to concentrate on big ideas? Or do you want them to focus on very specific operation/computation type games? Know your students and their level. It is very important you select a game that will actually benefit the student.

·         Make sure the game matches the mathematical objective

·         Use games for a purpose and not as a time filler

·         Choose a game that makes ideas concrete with interactive visuals

·         Make sure the games are engaging!

There is online YouTube video by Dr. Devlin. He offers parents and teachers important guidelines and four sources for locating high quality math learning games. 

References

Games for teaching and learning Mathematics | Engaging Maths. (n.d.). Retrieved October 23, 2016, from https://engagingmaths.co/2015/04/12/games-for-teaching-and-learning-mathematics/

Why Play Math Games? - National Council of Teachers of ... (n.d.). Retrieved October 23, 2016, from http://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Why-Play-Math-Games_/

The Art in Math

  

Reflection 5

                I got inspired by the drawing and representing math module to write this blog for today. The word drawing simply stood out to me and I thought why not connect art and math together? This idea can give a way to even incorporate cross-curricular activities. After I had this idea, I searched up ways to teach math with arts, and I definitely found many interesting ways to do that.

                I think teaching math with art is an excellent strategy. It can include diverse types of learners. Using art can improve retention of key concepts and vocabulary as well. If you incorporate art with math lessons you are engaging the students and they can also have fun at the same time.

Benefits of Drawing

                Do you remember times when you would read a problem again and again but you weren’t able to grasp it? Sometimes just reading a problem out of a text book can make you lose focus, especially if you are not understanding it. So, if you draw the situation, it causes you to internalize what the problem really is asking for. It can also help us how to proceed. The process of drawing out a problem can help students out in other subject areas too; it can also help them later down the road.

For example: a student is taking science in high school and it is on physics concept. Drawing a picture of every single problem in physics is really important. Drawing helps you put all the ideas together to make it concise and easy to proceed to the next step in solving the problem.

                Drawing acts as an intermediate step between language-as-text and the symbolic language of mathematics. By representing visually, students can start to think about the problem mathematically. Hence, drawing is an important part of mathematical communication.

Math with Art Examples

1.       Math Stories Here is the fun part of math, so how can you include art in math? I found a really interesting idea from a website called Teacher Support Force that mentions math stories. Math stories are about drawing a story out of a given problem to help a student internalize the problem. It can also help with memory, so that students are able to recall the concepts!

2.       Geometry When you think of the word geometry you think of shapes right away as well. Does shape have anything to do with art? Of course it does! Students can learn geometry by drawing and/or creating shapes themselves. This way they have experience doing it and can visually see it.

3.       Patterns You can have an activity with the students where you ask them to draw patterns that they see in the real world, such as the spirals on snail, and connect them to math patterns. At the end, they will see the connection between math and patterns in the real world. They will be able to recognize that math is all about patterns and you can see it all around you.

4.       Vocabulary If students draw the new vocabulary words that they learn in math they can retain it better as well. Here is a really awesome example:

Image retrieved online from Teaching Math With Art - Teacher Support Force. (2011). Retrieved October 22, 2016, from http://www.teacher-support-force.com/teaching-math-with-art.html

There are many ideas out there that can help you combine math and art. It can be really helpful for students who want to understand math concepts. It can gear toward diverse types of learners as well. It is an excellent learning strategy to learn for other subjects as well, inlcuding language- when you want to draw story boards for example.

References

Teaching Math With Art - Teacher Support Force. (2011). Retrieved October 22, 2016, from http://www.teacher-support-force.com/teaching-math-with-art.html

Gibson, J. Top 10 Strategies for Improving Math Grades at Any Level. (1998-2015). Retrieved October 22, 2016, from http://www.mathgoodies.com/articles/improve_your_grades.html

Problem Solving: Draw a Picture - TeacherVision.com. (2000-2016). Retrieved October 22, 2016, from https://www.teachervision.com/math/problem-solving/48931.html

Jigsaw Puzzles

Reflection 4

            

            A friend of mine today inspired me to start my blog for this week. I was on a call with her and she mentioned how she hates math. I then took the opportunity to ask her for reasons. Simply, she mentioned to me that math should be creative and interesting.  She said you have to make it interesting to get her going on math. That triggered a thought inside of me, and I started to think that really why most people dislike math is just that they don’t find it interesting.

            Now of course when you are a teacher you don’t feel right when someone says that they don’t find a particular subject interesting. It adds some guilt to the plate. However, it also then makes me feel more motivated and responsible toward future generations. Previous mistakes should not be repeated again. If in the traditional classrooms math was not interesting, it should be now. If it is still not creative enough, then really there is no change; we want that change happening though. 

            I certainly don’t want to be that teacher who makes students miserable in a math classroom. Who am I to take away from them the numerous career opportunities that can come with math? Why would I want to create an obstacle for students in learning lifelong skills that could be used in various fields?  When my students grow to become adults, I want them to say I enjoyed math. For that to happen, there has to be space for creativity.

New Puzzles Daily. National Geographic. (2016). Retrieved online from http://ngm.nationalgeographic.com/games-puzzles 

            I remember once teaching a grade 8-math class where I set up a separate station for jigsaw puzzle games. Every month there would be a new scene and a new set of puzzle pieces. The idea was  to observe all the different strategies that students can use when completing the puzzle game. Students got to work together and discuss ideas. They shared ideas and made mistakes. They also went back, learned, and corrected their mistakes to come to a final solution. These are all skills that you use/need when working on math problems!

When my students got exposed to that station for the first time, they were all very surprised. They all asked me questions/comments such as:

-What is this?

-Why are we playing?

-Do we really get to play? But then what about math?

-Are you serious?

-“Look! We have a game in the classroom, ssshhh we want to play later listen to the teacher.”

Comments such as the ones above really opened my eyes. Students were stripped away from fun and enjoyment in math classes. They had a thirst for something different. Their minds got sparked only because of a jigsaw puzzle game station. I was actually able to see excitement in the students’ eyes. That’s the energy that I want to see in every student’s attitude.

            Okay here are my final comments:

-       Jigsaw puzzle game is just a small idea that got students excited

-       There can be numerous other ideas to instill creativity in students

-       Math can be useful and fun at the same time

-       Know your students and try new things

-        Explain to them why they are doing math

-       Explain to the students about strategies, skills, and how they can connect it to the real world


  PS: I suggest this website if you want some fun jigsaw puzzle games that you could play with your students on your device. http://www.nationalgeographic.com/games/photo-puzzle-jigsaw/#home
        You could make it a cross-curricular with science by playing some of these games. 

Be Messy

Reflection 3

Top 5 Things to Look for in a Summer Camp. The Huffington Post. (2015). Retrieved online from http://www.huffingtonpost.com/tara-chklovski/top-5-things-to-look-for-_b_7429818.html 

Highlights

The highlight of this week’s class for me was the open ended questions. There was an activity in class where in groups we had to take closed ended questions and turn them into open-ended questions. I realized that open-ended questions give students a lot of room for thinking. Many students will have a variety of solutions for one question. This encourages thinking and creativity. This can also empower students to come up with their own strategies for a certain problem. When students become thinkers they would want to explore around. Exploring gives students room to make mistakes. Mistakes can take them to the correct solutions. Therefore, I think that mistakes shouldn’t be looked down upon, because it can grow brains.

Make a Mistake

Math is a world of mistakes. You are encouraged to try different ways, explore, experiment around, and have fun with the challenges that math can provide. Students should never be discouraged if they make a mistake, but they should be encouraged to try their ways differently. Jo Boaler says, the more mistakes you make, the more your brain grows. Students should be encouraged toward a growth mindset. All students should have a positive attitude and say, “yes I can do this!” for any challenge that is presented in front of them. So how can you allow your students to make mistakes?

·      Make a safe learning environment

·      Encourage students when they make mistakes

·      Have less competition in the classroom

·      Make your classroom a learning environment

·      Let students learn from each other

·      Create a respectful environment in the classroom

·      Come up with strategies that tell students making mistakes is okay

·      Encourage growth mindset

·      Show your students real life examples of people who became successful by making mistakes over and over again

Above is a list of ways that a teacher can use to let students feel comfortable making mistakes. Students should feel that if they make mistakes, they can learn from it. The journey does not end only when you make a mistake, but you continue experimenting until you get your “ah-ha” moment.

Not About Speed

Math is about quality rather than quantity. Some of the videos that I saw in the math mindset module reminded me of multiplication drills that I used to do as a student. Speed never taught me multiplication tables. I might have ended up just memorizing numbers, but never understood those numbers. At least I did not understand until I started to take my time and learn by myself. I have taught myself math throughout elementary school, because I never really understood anything from my classes.

I think that speed can intimidate students, and when you are intimidated you can get stressed. It is hard to think under stress. If you are fast are you really learning? Understanding math deeply is more important than how fast you can solve a problem.

I want to encourage students to think deeply about a problem so that they understand the core concept. If they understand the core concept they can then solve any problem at hand. In my future classes, as a future teacher, I want to make a difference in how math is taught to students. I want students to have fun and to like math as much as they would like any other subject.

References

Boaler, Jo. Mistakes Grow Your Brain. (2016). Retrieved online from https://www.youcubed.org/think-it-up/mistakes-grow-brain/

It is all About Growth

Reflection 2

Highlight of the Day

            This week’s class was very interesting. I got to play a card game on top of learning new tricks in solving math problems! I really enjoy my ‘ah-ha’ moments. They just click with me and then stay in my long-term memory storage where I never forget. So let me start off with what stood out to me the most this class.

The Shepherd Problem. Retrieved online from https://www.youtube.com/watch?v=kibaFBgaPx4 

The class started off with the shepherd problem. This problem was really interesting because it really shows that some students are not thinking when they are reading the problem. Students might think math is all about getting an answer whether it makes sense or not. They are not used to sitting back, relaxing, and thinking about the problem. Does the wording even make sense? Do I even need to solve the problem? This makes me think that for some students, having no answer to a problem means failure, so maybe out of this fear they would write down whatever answer they could get out of the numbers given in the problem.

This also makes me think, do teachers make an environment where students are fearful of making mistakes? How can I as a teacher take away their fear and let them stay stress-free? I really think that it is time to change the environment of math classrooms. I am really happy that I am becoming a teacher in this age. It is a great time to innovate, experiment, and grow to succeed. This takes me to a whole new topic that I really want to talk about: “Growth Mindset.”

Grow...

            Notice how earlier I mentioned: “Grow to succeed.” If you have a growth mindset you are likely to succeed as compared to having a fixed mindset. This concept is entirely new to me since I started teacher’s college. However, it is also becoming a very familiar topic that I am very comfortable with now. Deep down when I didn’t realize it, I also have a growth mindset.

It wasn’t until late high school and university that I realized I can do well in math when I practice often. It took me a while to understand that while facing ups and downs throughout the process. I used to believe that if I see a problem I could solve it right away. However, that was the case only with easy problems, but when it came to harder problems I was usually taken off guard. When I finally felt confident enough to start practicing problems after problems, I started to do quite well in math. All it took was the realization that all I need to do is practice, and then I can do well. It was not only about being smart, it was about practice and having room for mistakes.

I learned a very perceptive concept today as well, and that was not to tell students that they are smart. It will hinder their abilities and they would start to have a fixed mindset instead. Students will then just want to keep up with their smart image and focus on solving easy problems instead. I found an interesting article to read on ABC news that also mentions with hard work intelligence grows. The article that I read was written by Joy Phenix and it was called: “Why You Shouldn’t Tell Your Kids They are ‘Smart’.” Certainly, this idea is not an alien anymore, but is being incorporated in other places.

I want to instill that in my future students too. I want to make them feel that with hard work they can accomplish a lot. Sometimes just being smart is not enough, if you think you are smart, you will stop there; your growth will stop there. Then when you are faced with bigger challenges, you won’t be ready.

References

Phenix, Joy. Why You Shouldn’t  Tell Your Kids They are ‘Smart’. ABC News via Good Morning America. Retrieved online from http://abcnews.go.com/blogs/lifestyle/2012/02/why-you-shouldnt-tell-your-kids-theyre-smart/. Sept 18, 2016.

Go Deep!

Reflection 1

Before starting playing this game, do you ask yourself why is one box moving right and the other moving up?
Exercise your intuition.
Image retrieved online from http://gameaboutsquares.com 

Here I am back on my blog to talk more about math. To be honest, I never thought even blogging about math requires thinking about the main idea, just like thinking what is the concept behind a certain math formula. Well, after much thinking and reflection I think I am ready to share my thoughts.

I find my math classes very interesting, because I get to be two personalities at once: Student and Teacher. It is now not just about solving the problem, finishing it and handing it in for marks. Math is now about solving the problem to make it easier for our students. Math is now about finding different ways to solve a particular problem. Math is now about thinking from the student’s perspective and connecting it with the teacher’s resources. So how do I fit in as a teacher?

Can I solve the grades 4-8 EQAO problems with no difficulty? Yes I can, but can I solve it in a way that my student’s can understand it? Do I specifically understand how I solved the problem? Can I explain to myself why I solved the problem that particular way?

Math is all about ideas now. Whether I passed all my math classes in my previous school years including university level classes does not matter so much anymore. Math is not just about doing it now, but it is about why am I doing it the way I do it. I want my students to understand the idea behind it. I want my students to understand how they got to the results. I do not want it to be a ‘plug n’ chug’ class for them.

Now for students to be able to understand the idea of math, they have to have space for trials. Trials allow you to solve a particular problem few times by making mistakes. Yes! Making mistakes is key here. If someone out there does not agree with me, at least Jo Boaler agrees with me. In an article Gary Antonick mentions that Jo Boaler said the following to him:

“Good teachers have said this for a long time — mistakes help us. We can learn from mistakes. But this is a much more powerful message: that we can learn only from making mistakes. We need kids making mistakes. If kids are not making mistakes — if they’re not struggling — we’re limiting their brain growth....” (Jo Boaler: Mathematical Mindsets, by Gary Antonick)

I think students will make mistakes if they feel safe enough to do so. They will feel safe enough to make mistakes if they do not fear something. I ask myself sometimes what could students fear the most in a classroom setting? I think it is punishment, getting put down, being looked down upon or being made of fun. It is easy to be made fun of in a math classroom. I think it is up to the teacher to eliminate all of that and make it fun for everyone. If they solve a problem wrong they should not get penalized for it, let them play around with it, discover, think, and be messy! It will get them somewhere.

References

Antonick, Gary. Jo Boaler: Mathematical Mindsets. The New York Times. http://wordplay.blogs.nytimes.com/2016/04/18/boaler-math-mindset/?_r=0. April 18, 2016.