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.

Weekly Report & Reflection Week #11!

Reflection 11

In the second last session of this math course, we started to look at formative assessment. One good question came up was that how do we assess students using the "As Learning" format. Let us give an overview first of all the assessment types. 

From the Growing Success policy document: 

Assessment FOR learning is more commonly known as formative & diagnostic assessments.  Assessment FOR learning is the use of a task or an activity for the purpose of determining student progress during a unit or block of instruction.  Teachers are now afforded the chance to adjust classroom instruction based upon the needs of the students.  Similarly, students are provided valuable feedback on their own learning.

Assessment OF learning is the use of a task or an activity to measure, record and report on a student's level of achievement in regards to specific learning expectations.  These are often known as summative assessments.

Assessment AS learning is the use of a task or an activity to allow students the opportunity to use assessment to further their own learning.  Self and peer assessments allow students to reflect on their own learning and identify areas of strength and need.  These tasks offer students the chance to set their own personal goals and advocate for their own learning.

So looking at the assessment as learning, you can see that it is all about self assessment. How can students self assess in math? Here is a simple example, give them a problem, and tell them what do you already know about this. This will allow the students to self assess and ask themselves all sorts of questions by bringing up their past knowledge in trying to solve the current problem. 

In this session of week 11, the instructor modelled for us how to self assess. He gave us the 5 fingers problem similar to the one below:

Tom likes to count on the fingers of his left hand, but in a peculiar way.  He starts by calling the thumb 1, the first finger 2, the middle finger 3, the ring finger 4, and the pinkie 5, and then he reverses direction, so the ring finger is 6, the middle finger is 7, the first finger is 8, the thumb is 9, and then he reverses again so that the first finger is 10, the middle finger is 11, and so on. Where would number 1000 land (on which finger)

So he had us solve the problem first on our own, then asked us what we go to and how, then he prompted us further and asked why we got there. Then the instructor solved the problem on the board by asking us as a class too (guided teaching).

These problems can be used from grade 2-12. Depends how complicated you can go with the solutions. The solution can be as simple as just counting, or as complicated as making algebraic expressions. 

There are such problems on the:

Collaborative Mathematics website, click HERE.

Math Counts website, click HERE. 

Important notes:

Challenge kids
Let the students do the work

Weekly Report & Reflection Week #10!

Reflection 10

In this week's session we had covered the topic of probability. Probability can be easily dismissed and sometimes be labeled as common sense, hence we do not need to study it. You can, however, think of probability as common sense put into calculations. 

"As with other beautiful and useful areas of mathematics, probability has in practice only a limited place in even secondary school instruction" (Moore, 1990, p. 119). The development of students' mathematical reasoning through the study of probability is essential in daily life. Probability represents real-life mathematics. "Research in medicine and the social sciences can often be understood only through statistical methods that have grown out of probability theory" (Huff, 1959, p. 11). Moore (1990) stated:

"Probability is the branch of mathematics that describes randomness. The conflict between probability theory and students' view of the world is due at least in part to students' limited contact with randomness. We must therefore prepare the way for the study of chance by providing experience with random behavior early in the mathematics curriculum."


From reading the quote above it is understood that students are mostly exposed to structured and organized matter around them. They are not exposed to taking risks and being random. So how as a teacher can you expose randomness?


Have students just play with dice, cards, different colours and other objects randomly. Have them explore what it means to role dice randomly and predicting what the outcome will. Probability can even be taught through other mediums that can pick up the students' interest and motivation. Use technology that can include different apps and games that can teach probability. There are many interactive probability games over the web. 


In our class this week, my classmate and I created a presentation that introduced concepts of probability through an activity using coloured marbles and Kahoot. We used Kahoot to do a quiz/survey with the whole class using probability terms such as: Likely, Unlikely, Certain, Impossible and etc. We observed that Kahoot can be a very interactive and fun way to teach students something because they can get excited in a friendly and safe competitive environment. The coloured marbles activity was also fun and simple where students get to use different manipulative to learn probability concept rather than sitting and listening to a boring lecture from a teacher. 


Here is a fun that you can teach probability to students: using M&Ms!! Who doesn't like chocolate?

Weekly Report & Reflection Week #9!

Reflection 9

This week's session we started the class with the instructor explaining to us a math portfolio that we have to create. After that our classmates started their learning activity presentations. The focus for this session is measurement. The presenters showed us the "Perimeter Around The Area" video, by the Brazillions, on YouTube. Watch below:

After we watched the video we played a game board using dice and shapes. It was a fun game but was not too sure how it related to area or perimeter. It would probably be a good game for a "Minds On" activity. The second presentations was also for the measurement unit but focused on circles (circumference and diameter).

We started by the string and circle diagram activity. We took the string and measured the circle with it and recorded it as the circumference. Then we measured the diameter of the circle with a ruler. We divided the circumference by the diameter and got a number very close to 3.14 but not exactly that, as it was an approximate, but we did not get a  number that was very off, so it was good. This activity introduced us to the number pi. 

Then we did another activity with toothpicks and a piece of chart paper. It introduced us to the concert of pi in degrees which is 180 degrees. It was all about the rotation of toothpicks! Awesome activity. I think these activities would definitely be useful for me as my teaching block this January would be all about circles. It would include circumference and area with some other concept. I am teaching grade 8 so these activities are definitely applicable. 

We got referred to YouTube channel: Numberphile for more ideas, by our classmates. 

This was the end of the second presentation followed by a third presentation. Also focused on the measurement strand, but is on a different topic, called time. We worked through a story that had a math problem in it. Using a timeline we figured out the answer. It was a good activity focused for the younger grades. 

After all the presentations we started a jumping activity. Which was great, I think if that is applied in a classroom it would be great to help students estimate and find actually measurements from the jumping activity. It can also help students measure using non-standard units rather than metric. Definitely a very fun activity which involves measuring too using different standard or non standard units. 

Reflection 8

Reflection-8

This week's session was very informative. We learned a lot about geometry and spatial sense. It is a great, challenging, and fun topic. As educators, we might come across this question from students: "Why do we need geometry in our lives?" We need to be prepared to answer such questions. We need to believe geometry is important first before passing on the knowledge to others. So After some research, experience and my own thoughts I came up with a list:

1. To be able to understand the wonder of the worlds shape and appreciate it, we need to be able to understand and have knowledge of spatial use. 

2. Geometry will assist us in understanding the relationship between shapes and sizes 

3. Some people think in shapes and sizes, others think with visual abilities

4. Science and technology require knowledge of geometry

5. Geometry helps bring together both sides of your brain. The left-brain is more logical, technical, whereas the right-brain is the part that visualizes and where the artist gets their creative inspiration from

6. In the fields of television, moves and even little things like puzzles or books all are influenced by geometry

7. Geometry gives us a base for students to make sue of concrete materials and activities.

There are many other reasons of why we need to study geometry, I only listed a few above. 

From our class this week, the presentations taught me something new. It is that we can teach the math curriculum only through geometry itself. We can incorporate shapes in all of our lessons. How amazing can that be? Mostly, in the early years, geometry is taught through shapes and solids. Other topics within geometry include:

1. Line and segments

2. Shapes and solids

3. Triangles and angles

4. Platonic Solids

5. Coordiniate Grids

6. Radians

7. Conic Sections

8. Circumference

9. Polygons

10. Trignometry

There were few manipulatives introduced by classmates and the instructor that we could use in our lessons. It is best to have solid shapes as examples to show and teach the students about faces, vertices, edges and angles. The instructor also put up some puzzle games and another great OSMO iPad game kit. It would be a great station to have in a classroom for the students to work with. See picture below:

OSMO Kit. Photographed by Samia Sharif.

Other games:

Puzzles. Photographed by Samia Sharif.

Weekly Report & Reflection Week #7!

  Reflection 7-

Algebra

       

            This week’s topic in math class was algebra. My classmates did two learning activity presentations on this particular topic. Today’s presentations made me realize that I can reach an answer right away without focusing much on the process to the answer. However, students need to learn the process rather than the answer.

 I as a teacher candidate need to focus on the process of math problems. I need to learn how to break down problems for students. One problem can have many ways to get to the answer. At elementary level students can have many resources to learn particular concepts, in other words these can be called manipulatives. For example, the instructor today gave us blocks to come with an algebraic expression for a particular hexagonal pattern. We found an expression for the perimeter of the blocks.

Another way I have seen before to model algebraic equations is through the balance! I think it is a great visual to use when teaching. See example below:

 

Math is Fun. (2015). Introduction to Algebra. Retrieved online from https://www.mathsisfun.com/algebra/introduction.html

I realized that using variables for an algebraic expression could be confusing for some. So how should we explain to students why we use a letter? I found a simple answer to that from Math is Fun (mathisfun.com).

·      It is easier to write ‘x’ than drawing empty boxes (unknowns) (and easier to say ‘x’ than the empty box

·      If there are several empty boxes (several unknowns) we can use a different letter for each one

·      So x is simply better than having an empty box, but any other letter can also be used

I think it is interesting how our class is grouped rather than single desks for each of us. This way is great because we get to learn a lot from the people in our group. I would definitely implement this kind of setting in my classrooms in the future as a teacher. Hence, this was the first half of our session today.

The other half of our session today was lesson planning. We took our drafts of lesson planning today to the instructor for him to look it over. I have some areas where I need to touch up on. Lesson planning is an exciting part of teaching. It is the core of our teaching service. If the lesson plan is good than teaching, classroom management, and outcomes can be great as well. I want to gain the confidence to lesson plan and I am looking forward for it to become the intuitive part of me as a teacher.

According to the instructor, after much experience, the implementation of lesson planning will be become engraved in me as a teacher that I wouldn’t even realize that I am taking those certain steps. These thoughts are however for the future only, but what about the present? Our time for internship is coming up fast and I am nervous to teach because I want to put my best out there rather than getting confused.