WEEK IV

Hello everyone and welcome to my week 4 math post!

During the past few weeks in my math class at teacher's college, we have been learning many ways to enrich our instruction as teachers, so that we may benefit all of the students in our classrooms. Today, I will be highlighting some more of my learning experiences and how I plan to integrate them into my teaching! I hope you enjoy! 😀

Out With the Old, In With the New (and RICH!)

It strikes me every time how different our students' learning experiences are today, compared to when I was a student myself. The way we teach math has evolved into so much more than just worksheets, teacher lectures, copying notes and independent work. Now, educators aim to teach math in a way that is...

• relevant, 
• current, 
• challenging, 
• collaborative, 
• engaging, 
• has depth, 
• fosters deeper thinking, and is
• student oriented.

I will elaborate on how having these components in a math class creates rich tasks shortly! But I know that when I was a student, I did not always have these types of rich math scenarios. Oftentimes, we would end a unit with a unit test, and that was that. Now, teachers strive to develop these rich opportunities for students, and they also try to finish math units with rich culminating tasks, as opposed to tests. There is a time and place for everything, however, and I believe students will also benefit from taking a test, or two. When I teach in my next classroom, my goal will be to shift away from the: teacher lecture → independent worksheet → test strategy, no matter how tempting! Because hey, it is what I was brought up with! Having students talk to each other about math and work together on rich problems really improves their overall learning and understanding.

Below, I am going to talk about some other strategies and ideas for enriching student learning in the class. I will also share some of my experiences with these strategies!

Talking About Math and Making Connections

Art and Math. (2018). Image. Retrieved from: http://discovermagazine.com/mathart

When students talk about their math work, they are able to communicate different approaches to the problems they face. Again, when students just work independently, they may not have opportunities to understand the many pathways that could be taken, or the many questions that could be asked about the math problem.

Reflecting on my experience with math talks, I recall several times where this was put into practice. One experience I remember was having students volunteer to share their work to the class and display it under a document camera, for example. The class then began a math discussion and students could see and hear the different types of reasoning used in the math problem. This is great for differentiating too because it lets all learners actively participate as they compare and contrast their reasoning with their peers! ANOTHER type of math talk that was done during my last placement was having students take up their exit tickets in their groups. The way that I would have done this a long time ago as a student in math class would have been a) the teacher would have taken it up in front of the class, b) the answers would have been posted on the board and we would have checked by ourselves or c) we would just ask the teacher any questions we had during class time or recess. Thus, having students work through their exit tickets together is another type of math talk, where students analyze the problems and discuss their reasonings behind it!

Rich Math Performance Tasks

According to Steve Hewson's article titled, "What is a Mathematically Rich Task?" (2011), he states that rich tasks allow for, "[a] resulting learning process is far more interesting, engaging and powerful; it is also far more likely to lead to a lasting assimilation of the material for use in both further mathematical study and the wider context of applications". In his blog, my colleague Tyler also believes that rich tasks allow for collaboration and discussion and that, "[...] in a math class, or any class in general, collaboration and discussion really drive learning and are linked to inquiry". The short video above also goes into further detail about rich tasks. Take a look!

Here is an example question:

Word Problem. (2018). Image. Retrieved from: https://nrich.maths.org/895

As I described before, this question would be an example of a rich task. Teachers could even bring these manipulatives (marbles) to school as well, to make it even richer. There are many ways students can approach this! NRICH has a great collection of rich tasks to use in the classroom and I will definitely refer back to them when in my next placement. Another resource I found that will be great to refer back to is from YouCubed! Check them out!

A final reflection for today would be about one thing I vividly remember during placement. We were summing up the math unit I was teaching and I decided to end it by doing a story problem. Students were engaged and loved the real life applications, along with the time they had for collaborating in order to solve this rich task that was presented as a fun story!

Closing Thoughts

So far I have been learning even more about differentiating, making math meaningful, the importance of making connections, having rich tasks and allowing for discussions and collaborations about the big ideas in math.

Please come back next week, I have a feeling it will be worth it to do so!

Love,

Teddy

W33K 3

It is WEEK 3 friends! And that means that we are at exactly 50% of reading my blogs for my math learning at teacher's college! Bittersweet.

via GIPHY (Yes, Simon Gibson. We feel the same way about it being Week 3.)

Question: What is another way to express 50%? 

(Have a few, or many minutes to think.
DID YOU KNOW: Time does not determine how good you are at math!)

Answer: We can express 50% several ways. One way is by fractions: 50/100, and when we find the lowest common denominator, 1/2. We can also call 50% as one-half. Or, we can write it as a decimal: 0.5. We can show this idea visually too, as seen in the image below, with a circle! ↡

Fraction Circle. (2018). Image. Retrieved from https://sites.google.com/a/kcusd.org/5th-grade-fraction-projects/group-2.

Fellow math scholars, there are maaaaany ways to show this concept. You could have shown half of a banana. Or maybe 50% of a pumpkin pie you ate, or half of a pumpkin spiced beverage you drank! There is NO right answer, because, well, they are ALL right and they are ALL connected.

Now, let's get into an interesting topic and break some more crazy math stereotypes. 

Speed Does Not Determine A Student's Ability To Learn, And Mistakes Are Okay!

There are different speeds at which people learn new things, especially math! Do not feel that if you are a slower learner, you have slower or smaller intellectual capacities. In fact, speed does not determine a student's ability to learn and is only a factor of how they absorb, make sense of and process information. Making mistakes in math is also totally okay and sometimes even necessary. Science shows that when mistakes are made, the brain works hard and that hard work creates new brain connections. This actually make the brain grow! So even if you make a mistake, keep trying, your brain will grow as a result! GROWTH MINDSET!

In this video, a really famous person who was a slower math thinker is revealed, can you guess who?

Differentiated Instruction

This new and important information definitely has implications for teachers that are preparing for diverse learners in their math classrooms, since students' math speeds can vary significantly. Capacity Building Series: Differentiating Mathematics Instruction (2008) states that allowing for the right amount of time, or extra time, during math work should be a part of a teacher's differentiated instruction. 

Because differentiation can be challenging, here are some teaching strategies I have discovered that might be helpful in a math classroom.

Differentiating With Open Ended And Parallel Tasks In The Math Classroom

We talked about math centres last time using the Math Daily 3 approach. Today, we will discuss open-ended questions and parallel tasks. 

What are Open Ended Questions?

Open ended questions are questions that allow students to make a choice about the numbers, ideas and strategies they will use to answer a problem. The question is set up in a way where the students will reach the same "big idea" and curriculum component, although each student will get to make a choice and thus, will have a slightly different answer. Consider this example for Grade 5 Patterning and Algebra below:

Q: "Create and draw a pattern that has two steps (i.e., multiply by 2 and add 3). Then, show 2 different ways to represent your pattern (i.e., numerical, in a table, etc.)". 

The teacher is asking for the same "big idea", but is allowing the student to create their own version of the question. This is good for differentiating because students do not feel trapped by a fixed question and can use the numbers and strategies that are at their level of knowledge and skill. This also gives them a feeling of autonomy.

What are Parallel Tasks?

Parallel tasks are similar to open ended questions and are two or more questions provided by the teacher that meet the same big idea, however, are catered to the different math knowledge levels of the students. Teachers create and then look at the question they have posed to students. Teachers then anticipate where some students might struggle. In the parallel task(s), the question(s) are modified to erase those areas of difficulty in order to meet the needs of different learners and allow them to succeed at the question the teacher would like them to solve.

This week, we created a parallel question/task to this question given to us by our instructor: 

Q: "90 students in a school have gone to at least two other provinces.  If this represented 24% of the students in the school, how many students are in the school?"(Bunz, Rebecca, 2018).

We anticipated a few challenges that students may face within this question.

1. The wording (too wordy, let's reduce the words, or make them even more challenging) &
2. The numbers used (let's use smaller (or larger numbers for high ability students)).

The parallel task we created was to differentiate to the lower ability students, or to English Language Learner (ELL) students, and it was:

Q: "100 students go to the same school. If this represented 50% of the population, how many students, in total, go to the school?"

So essentially, students are working with proportions and percentages, which hits the big idea that the teachers needs to cover in the curriculum! BUT, we used friendlier numbers, that had an obvious relationship with each other (i.e., 50 and 100, as opposed to 90 and 24) and also used less words. (Note: depending on the math abilities with ELLs, the numbers might not have to be changed, just the wording). Teachers could make the components of the question easier, or more challenging to differentiate to all learners in the classroom. Parallel tasks are questions that are usually not open ended, although they could definitely be modified to be a mix of the two types!

To further highlight this differentiation process, here is a link from The Learning Exchange to a great video that explains these two concepts again, provides examples and shows students using these methods in an actual Ontario elementary classroom!

I hope that this week helped you to continue understanding some negative math stereotypes. I also hope that you have some new ideas about differentiating instruction in the math classroom! 

That will be all for this week scholars!

Much love,

Teddy 

W33K 2

W3lc0me b4ck 2 w33k 2 fr13nd5!

This week, I will be highlighting the growth mindset, and I will also be talking about a strategy to differentiate math in the classroom. Keep reading below! ⇩

                                                                             (can you spot the math probability language?)

Firstly, I would like to make a guess and state that chances are, you, the reader, have been most likely impatiently waiting for my blog this week, because you really wanted to know about this game-changing mindset I briefly mentioned last week (and maybe in my previous math blog)...

AM I RIGHT?

Well friends, your odds are great because I am 100% certainly going to discuss it with you (again), as promised. Behold, The Growth Mindset! 

The Growth Mindset and Math 

Growth Mindset vs. Fixed Mindset (2018). Image. Retrieved from https://believeperform.com/product/growth-mindset-vs-fixed-mindset/

You NEED to be reminded of the growth mindset. It is very important. Period.

Let's start with the opposite of the growth mindset: the fixed mindset. With this latter mindset, students learning math believe that they have inherited fixed math abilities. That means they believe that no matter how often or hard they try, they will simply never succeed at math. They also believe that people are either born to be good at math or are destined to fail it. Those that believe they are destined to fail have a hard time with math, because they disengage and begin hating the subject entirely. They then spread this idea to others and the cycle continues. Sounds gloomy and somber to me. I believe this mindset needs to be erased from our students' minds!

Now, the growth mindset, the game-changer. This is the mindset that allows positive thoughts to move through our brains. Scientific studies have proved that everybody's brains can learn and grow when doing math. It is a matter of hard work and dedication that determines a person's ability to do math. The harder your work and the more you practice, the better you will get at whatever you are practicing, especially math! The growth mindset means that you believe your abilities can grow if you do not give up trying. That is, staying positive, believing in your self and working hard for your goal WILL pay off in the end!

This has serious implications for educators and specifically for math teachers. Math teachers need to help their students succeed by pushing them and telling them that they are capable, as long as they are willing to work through challenging math concepts and problems. Teachers need to model this behaviour as well to fully promote its effects. An example of this would be to be careful when naming students as being 'smart'. We learned that students who are praised for being 'smart' develop a fixed mindset and easily give up when challenged. Not only that, but this also makes other students feel inferior and they might also develop a fixed mindset as a result.

Below is a truly inspirational video that I would like to regularly play for my students in order to remind them about having a growth mindset and never giving up!

Differentiating Math in the Classroom: Math Café Daily 3

This is a subject that can be written about for days. It is something that I, and many teachers, find challenging to do. In their article titled "Using Math Stations for Commonsense Inclusiveness" (2012), Janet B. Andreasen and Jessica H. Hunt describe differentiation as, "[...] a process through which teachers enhance learning by matching student characteristics to practice and assessment" (p. 240), and discuss that differentiation "[...] is one way to make the success of all students in mathematics a reality" (p. 238).

There are so many diverse learners (i.e., visual, musical, kinaesthetic, etc.) in any given classroom. Teachers have the job of recognizing these differences and creating instructional strategies that allow all learners to be successful in the classroom. A strategy that will help teachers differentiate their instruction in a math classroom is called the Math Café Daily 3.

The Math Daily 3 approach provides centres with different activities for groups of students to do. Usually they are:

Math by Myself - In this centre, students work on independent activities that strengthen their core understanding of the math unit they are working on.

Math with Someone- Here, students work with a partner with a focus on collaboration in identifying math thinking skills and organizing math problems, for example.

Math Writing- Students work through communicating their thinking and understanding of math problems.

...and sometimes a 4th centre: Math with Teacher- Here, students that need extra guidance work with the teacher to check-in with their understanding.

Sample of Math Daily 3 Rules (2018). Image. Retrieved from https://turnerteaching.wordpress.com/math-lessons/

Math Daily 3 centres might have different levelled activities at each centre, for students with different abilities to work through. Students will be assigned groups and will rotate through the centres until they have completed them all. This method allows them to work through their various math processes and skills and try different types of math work and problems. It is a great way to differentiate math in a classroom! Above is a sample of some Math Daily 3 rules before students get started in their centres. Take a look!

Concluding Thoughts

This was a very content heavy post, but it was necessary! We touched on the growth mindset and differentiation in math classrooms. Two scorching hot topics in education. I hope this post has inspired you to never give up!

Please keep checking for my next post, it is coming soon!

Thanks for reading!

Love,

Teddy 😁

W33K 0N3

Hello fellow math friends!

Welcome back to Teddy's math journey blog!

Quite the Math Journey So Far!

Math (2018). Image. Retrieved from http://www.loving2learn.com/topics/math.aspx

I would like to welcome you to the second part of my math blog. If you have been following my journey with math education since last year, you would already know that I am a current teacher candidate studying how to become the best math educator I could possibly be! I would love to teach in the junior/intermediate strand, and to be quite honest, I would not even mind teaching a high school math course one day! With that being said, the Grades 1-8 and Grades 9-10 Ontario Math Curriculum, however, actually differ from each other. In the elementary grades, students learn 5 strands of math. These strands are Number Sense and Numeration, Measurement, Geometry and Spatial Sense, Patterning and Algebra & Data Management and Probability. Each elementary grade builds on prior knowledge while introducing new concepts to each math strand. In Grades 9-10, math gets divided into the academic and applied pathways. Students in academic math begin visiting topics that might be expected for university prep and Calculus, for example, topics like analytic geometry. Applied students learn math skills that will be transferred to either colleges or the work place. In addition to these strands, there are also several mathematical processes that students are expected to follow in their math learning and these are valid across all grades, from 1-12. The Ontario Curriculum explains that these processes are important and they are as follows:

"The mathematical processes that support effective learning in mathematics are [...]:
• problem solving
• reasoning and proving
• reflecting
• selecting tools and computational strategies
• connecting
• representing
• communicating
The mathematical processes can be seen as the processes through which students acquire and apply mathematical knowledge and skills (p.11)".

I believe that these skills can help students succeed in other areas of their lives as well as in math. Mastering these skills helps them to learn how to work both logically and creatively!

So friends, now that I am in my second and final year of teacher's college, I have so much to tell you about the wonderful discoveries that I have made about math education so far. Some of these great discoveries have positively changed the way that I think about math and I truly can't wait to help my future students ALSO think about maths in this positive light! First, we will discuss how some math stereotypes have helped shaped our perceptions of the subject.

Rewriting the Math Stereotypes


via GIPHY

Well then, let's get straight to it! I have had my first set of math classes last week and I already have a lot to share and reflect on. Last week, we worked on understanding some serious misconceptions about math. What stood out the most to me was a video that showed how negatively math is portrayed in popular culture. This can be very detrimental to our current students because they rely heavily on media and the internet. Math is predominantly portrayed as a "nerd subject" and most people are quick to comment that "they suck at it" and "hate it". The video titled "Hollywood Hates Math" highlights moments in some memorable movies and television shows. Do you recognize any of these scenes?

I also had to recall that moment where Lindsay Lohan had to risk social rejection when she joined a competitive math club because she was great at math in the movie Mean Girls! And that movie is from more than a decade ago! Ultimately, these scenes help to perpetuate a societal narrative in which math is a hard, boring, uncool, lame and meaningless subject.

THIS IS NOT THE CASE!

Math can be learned by anybody and can be really meaningful. We need to start looking at math in a positive light instead, to help our students develop a better mindset towards math. A mindset where they know they can succeed and will work hard and never give up to do so! Next week, I will get into that topic and we will discuss the power of the growth mindset. I believe this mindset needs to be discovered by every single person on this planet and THIS exact mindset is what I hope to embed into my students' brains one day. Toon into my next post to find out how I plan to do this! 😀


S33 y0u n3xt w33k!


Teddy