Week 4 Report and Reflection

Week 4 Report and Reflection

Math drills, tests and uncomfortable speed tests were the reality of mathematics in my childhood. As a result, I become a fixed mindset, pessimistic individual that disliked math. It wasn’t engaging, and it certainly wasn’t fun. I struggled to see the relevance to my personal life let along the connection between concepts. Everything appeared to be abstract and full of algorithms. I hardly understood the concept of WHY something was done and simply memorized HOW to do something. I was often discombobulated and discouraged. Today, educators have the opportunity to change the discussion of math once and for all. We can emphasize relational understanding in the form of relevance and understanding the ‘how’ AND ‘why!’

One way to engage all learners, make math relevant and make it accessible to all learners is by providing students with rich tasks in mathematics. Rich tasks are real-life tasks that have multiple approaches and representations, encourage collaboration and discussion, and provide opportunities for extension. Rather than memorizing algorithms, facts and procedures, students can apply this knowledge in real-life contexts. Rich tasks can also be differentiated to need the needs of all learners—no matter the level! If students feel engaged in a task that they can personally connect to, they are more likely to do well and understand why things work the way they do.

Feeney, Cynthia. (2014, August 15). "Math By Myself"
Retrieved from

One aspect of rich tasks is incorporating discussion and collaboration with one another. This week we looked at a video in our module that explained that students who talk about their math do well because they discuss their strategies and their reasoning behind it. Even if the problem or work is wrong, their discussion can spark a pathway that can lead them to the path of other ideas or understandings. By discussing a choice of strategy and the work behind it, students can gain greater insights and understandings of the math because they’re able to explain it. Math daily 3 and math congresses are some great examples of how we can incorporate more discussion and collaboration in the classroom.

Feeney, Cynthia. (2014, August 15). "Math With Someone"
Retrieved from:

Feeney, Cynthia. (2014, August 15). "Math Writing"
Retrieved from:

Rich tasks can be set up in a number of ways so that they can be differentiated to meet the needs of every student. By using rich tasks and differentiated it, all students are able to develop the same skills but their pathway to get to that concept or understanding looks different for everybody. This relates to the idea that everyone can do math and that math is for everyone! Rich tasks are allowing us to make math accessible to all our students. In my classroom, my goal is to know my students and take their preferences and learning styles into consideration so that I can plan accordingly.

Rich tasks also allow students to represent and approach problems in multiple ways. Students can use their previous knowledge to help solve a problem. For example, in our module this week, there was a video that showed the connection between using similar triangles, geometry and transformations to look at and teach about equivalent fractions. I found this eye opening and informative about the importance of teaching math using connections rather than teaching concepts in isolation. See this video below for more information: 

One thing that I will also take away this week is the importance of including my student’s experiences in the classroom as much as possible. Something as simple as including their name in a math question can make a student feel excited and engaged in wanting to complete the problem.

Until next week!

Week 3 Report & Reflection

Week 3 Report & Reflection            

            We opened our class this week with a game called “I have…Who has?” which requires students to 1) answer math questions that people ask because the answer might be on their card and 2) pose the question on the card to everyone else. Each card has a match and the game is inclusive to all students. Teachers can strategically plan the cards according to the level of the student or have the students work in smaller groups. A generator for “I have…Who has?” can be found here. It’s a great resource for just about any subject!

Our topic this week was parallel tasks and open tasks as strategies to differentiate math. The underlying principle is that there should be a ‘big idea’ that could be addressed at different developmental levels using these strategies where students can also have a choice. The main difference is that in open tasks, teachers pose a single question that has a broad range of responses at many levels and in parallel tasks, teachers pose 2 different questions at different levels, but they are related according to the big idea and their context. 

            We got our first taste at doing these types of questions in class and I found it to be very successful in allowing any student the ability to answer the question according to their level. The Capacity Building Series has a great resource that has, using examples, more information about parallel and open tasks.

Capacity Building Series. (2008, September). Differentiating Mathematics Instruction. P. 5 [Retrieved from: http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/different_math.pdf]. 

Capacity Building Series. (2008, September). Differentiating Mathematics Instruction. P. 7 [Retrieved from: http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/different_math.pdf]. 

            After reviewing this week’s module, I learned that it’s important to work on challenging math problems that encourage students to struggle so that they can learn from their mistakes. It’s also important to make mistakes because a student might notice a concept or pattern that they wouldn’t have seen otherwise, or a student may understand why a method didn’t work. As a result, students would be able to talk about the problem or concept better. We need to encourage students that mistakes are opportunities for growth. 

            I know that things don’t always come easy, and most things require a lot of practice. Math is very similar to art in the sense that they both take time and practice. Your best art piece may take many attempts and will take time to get just right. Similarly, being good at math does not mean being fast at math. Math requires time to process and understand the concept. This is something to consider when we are testing our students. We wouldn’t put a time limit on students completing an art project so why would we put a time limit on a student’s processing time during a test? Placing a time limit for testing is often difficult for students who need time to think deeply and critically. Similar to open and parallel tasks, time allows students to go at their pace and level to meet goals in ways that suit them best. 

            Just like in art, there is more than one way to showcase something. The same is true for math. Being open to different experiences is an approach that students can use to recognize that there is more than one way to do something. Learning 1 algorithm is not the only solution to most problems. By being open to different experiences and ways of solving mathematical questions, students will be able to build a deeper and fuller understanding of concepts and big ideas. 

            The last thing we looked at this week was asking common questions and scaffolding questions. It’s important to help our students by asking questions related to the problem they are solving by using a common question or a specific question related to the problem without telling them the answer. The point is to allow students to think for themselves but make them aware that the teacher is there to help by guiding their thinking. As our teacher Pat said, "Be LESS helpful...but at the right times." Students shouldn’t feel like they can’t do something. Educators need to encourage students to foster a growth mindset using the word YET—they may not be able to do it yet. 

Week 2 Report & Reflection

Week 2 Report & Reflection

            What kind of tree does a math teacher climb? Geometry.

    This week one of our emphases was on making geometry approachable in the classroom and one of the lessons I learned is to always use hands on activities with geometry. Students need to be able to visualize and understand why something is the way that it is by physically creating it. By doing math, you can understand math. 

    I was very engaged in one activity associated with geometry and that was making a 3D structure out of linking cubes based on the front, side, and/or back views in a 2D picture. We needed to figure out how many owls were in the structure in total. I really connected to the activity because I like everything related to owls, so my attention was caught right away. Here were the 2D pictures, and the final 3D shape that my partner and I made:

McEachren, Patricia. (2018, September 10).
Week 1 slide #3. [PowerPoint Slides]            

Milhomens, Britney. (2018, September 10). 3D 
structure of linking cubes. [Personal Photo].

We decided to use green linking cubes to represent the owls, and yellow linking cubes to represent the blocks in the second row. If students know how to do the math, they are more likely to be able to explain the math, which results in understanding the math. Telling is not teaching.I need to consider this when I plan a unit plan—students need to be able to experience and do math before I am confident in their abilities to perform an algorithm. 

    Once students are comfortable doing the math, they are able to move into algorithms. A way to review algorithms and concepts used may be to use technology. One technological method we experienced in class was playing jeopardy and I found this to be extremely engaging for the whole class. It can be played in small groups, with a partner, or with the class and it is easy for me to create! This is definitely something that I will remember and use in my classroom in the future. 

    Another lesson I learned this week is to engage students with stories. I was engaged this week when Pat introduced a problem about kitten food and started talking about what kittens should/shouldn’t eat. It caught my attention and made me stay focused and I know that it will do the same for my students. 

Milhomens, Britney. (2018, September 13).
Kitten Problem. [Personal Photo].

     In that same problem, we were told to solve the problem in any way we wanted (except for using algorithms), and every group came up with something a little different related to proportional thinking. I liked that we got to consider alternative interpretations and solutions of the problem to be able to talk about it in a math congress group. A math congress is a group where you share and explain your strategy for solving a problem. This made me realize that there were many right ways to solve the problem rather than just one! This is definitely a good method that I will take into the classroom. 

    This method of teaching the kitten problem had many of elements of teaching math found in Principle 1 of the document “Paying Attention to Mathematics Education: Seven Foundational Principles for Improvement in Math, K-12.”  In the first principle, teachers need to engage students including using multiple representations of math concepts and use relevant math, encourage multiple approaches for learning/doing math and foster questioning (p. 4). All of this was done in one problem about kittens! Take a look at the article for further reading. One of my goals was to engage my students and I can definitely see how it can be done. 

   I learned this week that it's important to encourage hard work rather than telling students that they're 'smart.' It's important to tell students that you believe in them and that they are working hard in math! This will encourage them to want to challenge themselves and grow. 

     Until next week, mathematicians! 

Week 1 Report & Reflection

Week 1 Report & Reflection

            It’s my second year at Brock so I wanted to take this opportunity to welcome you all to my Mathematics blog- part 2! After my first class this week, I have to say that I’m already excited about what’s to come so stay tuned over the next 6 weeks! If you’re new to my blog or If you’ve followed my blog so far, you know that I’ve never been that comfortable with math and I was often told that I just couldn’t “do math.” This was one of the very topics that was addressed in this week’s math module. This week’s math module addressed many issues relating to attitudes toward math, math myths, brain growth, and smashing stereotypes. 

From past experiences and from watching various videos, people often dislike math, foremost, because it may make people feel "dumb" which is often the result of not being able to solve a problem. Additionally, people may dislike math because they don't see a point in it- the "why" behind what they're doing. People often dislike math also because it isn't particularly exciting for them. Math is almost always made out to be something that people "aren't good at" or it's “complicated” and “challenging.” This doesn't motivate people to want to do math, let alone pursue it later on in life. It’s up to us, as educators, to engage students in math and create a growth mindset amongst our students to encourage the idea that THEY CAN DO IT! Stereotypes are meant to be broken; it doesn’t matter whether you’re a woman, a man, black or white, able or [dis]abled, EVERYONE has the innate ability to do math. Teachers can squash these stereotypes in the classroom. 

This is one brilliant scene from the movie, “Hidden Figures,” where an African-American woman in a segregated community during the space race solves equations for the trajectory of a space capsule for one of NASA’s Astronauts. All of the white, male engineers are stumped until this particular woman comes up with a solution. This scene shows that anyone can do math, even if it seems like the solution is coming from an “unlikely source.” This fantastic scene can be watched below:  

Amasuga, Mark. (2017, April 11). Euler's Method scene in Hidden Figures [Online Video]. Retrieved from https://www.youtube.com/watch?v=v-pbGAts_Fg

We started our math class this week continuing this discussion about ability to do math. We viewed a video with spokesperson Annie Fetter who expresses the importance of letting students express themselves and asking questions to students to allow them to think for themselves. This is something important to consider when teaching a math class. It’s important to ask kids what they WONDER or NOTICE rather than ask kids what they don’t understand. This lets kids know that their ideas are valuable and useful which might make them more inclined to enjoy doing math. 

Milhomens, Britney. (2018, September 8). Screenshot of

A Game About Squares. [Personal Photo].

Another way that students can enjoy doing math is by using technology and games in the classroom. Not only can this teach students about particular concepts learned in class, but it can also teach them about cooperation and collaboration. My class saw this first hand when we played a game called “A Game About Squares." At first the class was extremely focused and quiet, but eventually you can hear a buzz of excitement and collaboration amongst ourselves. Some people would ask, “how did you do that” or “how did you pass this level?” We all worked together and discovered different strategies and pointers that we otherwise may not have gotten individually. Math doesn’t need to be an individual subject- sometimes more heads are better than one. (SCREEN SHOT) This is definitely something I will remember and be sure to use in the classroom. 

One of my personal goals for my teaching career is to make math more engaging and approachable and one way I think I can do this is by incorporating collaborative activities and games into the classroom such as the one we played in class. It’s important that students are introduced to different ways to learn things and encourage the idea that there are many processes that students can use to solve a problem. Manipulatives and visuals are things that I like to incorporate a lot in the classroom, but I hope to incorporate more technology into the classroom. These are things that I need to consider when planning a unit plan and I hope to learn more about how to incorporate different learning styles and teaching tools to make a unit more engaging for students. 

One article that I find particularly helpful is by Edutopia entitled "6 Ways to Help Students Understand Math." It incorporates an explanation as well as video examples for each way that can show teachers how to teach math to a variety of students. The article expands on some of the ways teachers can teach math to students that I've briefly described here such as introducing topics using multiple representations and solving problems in many ways (and encourage students to share their ways of solving a problem and incorporate these ways because maybe you haven't thought of that way yourself!) 
Until next week, readers!