Week 4 Blog Post

Hello and welcome to this week’s math blog! It’s become quite evident, over the past year and a bit of teacher’s college, that one of the most essential changes made to teaching is the focus on enriching instruction in order to make classroom material more approachable, understandable and engaging for all our students.  One of the methods that can be used to do this was the focus of our classes this past week: Rich Tasks.

In my experiences as a student, when required to differentiate mathematical tasks for learners at different levels of understanding, teachers would often provide questions for the different levels of ‘ability’ of their students. However, not only does this approach not allow for the depth of mathematical understanding and thinking that students will need in their future, but it also completely contradicts the concept of ‘growth mindset’. Using rich tasks in the classroom is a method that teachers can use in order to provide material that is equally accessible for all their students and that allows for depth of understanding.

As per Steve Hewson’s article ‘What is a Mathematically Rich Task?’ (2011), using rich tasks in the classroom provides the opportunity for students to move away from memorizing and attempting to apply mathematical procedures to allowing learners to ‘get inside’ math. According to Hewson this is because rich tasks can enable students to do the following:

• Access and explore math at different levels of understanding
• Make conjectures
• Work successfully when using different methods
• Broaden their problem-solving skills
• Deepen and broaden mathematical content knowledge
• Make sense of underlying principles
• Make connections between different areas of mathematics
• See the role of mathematics within cultural settings      
• See the role of mathematics within cultural settings
   

      These are just a few of the benefits that Hewson listed in his article. Because of this I believe that it is essential for us as teacher to include rich tasks in our teaching as frequently as would benefit our students. In for a task to be considered a ‘rich tasks’ must be accessible to all learners, have real world application, lend itself to a variety of approaches and representation, collaboration/discussion, engagement/curiosity/creativity and opportunities for extension (6 characteristics of Rich Math Tasks by Audet, Lauren (2016)).  

For those of us who will likely need some assistance here are a few helpful links to aid you on journey to enrich your math task:

 1) The nrich.maths.org  website provides a bank of resources for teachers including Rich Mathematical tasks.  

2) The nzmaths.co.nz website also provides rich math tasks for teachers. 

3) Laura Candler's blog gives advice on how to transfer basic word problems into a rich task. 

Here is an example of how to change a basic word problem into a rich task:

Candler, L. (n.d.). [Apple Peeling Problems]. Retrieved September 30, 2018, from https://bit.ly/2Rdv5jG

Thanks for reading and see you next week!

Week 3 Blog Post

Hello Everyone and Welcome back to my week 3 blog!!

This week’s online module focused mainly on the importance of making mistakes in math class and how mistakes allow students to improve and deepen their mathematical understanding. As I’ve already stated in my previous blog post I believe that it essential for us as educators to create an environment in our classroom that encourages students to take academic risks. By creating this environment, students will be more likely to take chances, makes mistakes, discuss their mistakes and thereby gain a deeper understanding of the mathematical concepts they are learning. So exactly how does one create a safe learning environment that encourages students to make mistakes and to see mistakes as a good thing? I believe it is a combination of classroom management, modeling, asking the right type of math questions, and the educator’s attitude. I also came across and interesting website that offers a lesson to help educators guide their students to this kind of thinking.

Click HERE for further information about this lesson .

In terms of asking the right type of questions, there are many ways to making math more accessible and more about the process than the answer. I mentioned the ‘math congress’ approach in my previous post; this week we discussed ‘Low Floor High Ceiling’ activities. These types of activities have open-ended questions and provide an opportunity for all students to access the learning material at their own level; they can also be extended however to higher levels. LFHC activities are great for inquiry-based learning and for a focus on a deeper conceptual understanding of mathematical process, which was a big part of my blog last week.  Click on the below link to find out more about these kinds of activities.

One final point I would like to reflect on is a piece of advice given to us in the classroom. We were told to ‘Be less Helpful’ with our students. Though, at first, this may seem not only counter-intuitive but also counter-productive to generating a health growth mindset in our students; I do agree with it. I believe that, by strategically directing students to get help from peers or to reflect further on their own, you are not only empowering your students to each other but you are also fostering in them the confidence to take their learning into their own hands. Being overly helpful with students can only be a hindrance in their learning, as it will likely prevent them from making the mistakes they need for the brain to grow. By allowing them to ‘figure it out’ you are giving them the opportunity to try different things, to make mistakes and even to be more confident problem-solving and sharing the discussing wrong answers with their peers.

Thanks for dropping by!!

Nadine Zahabi

Week 2 Blog Post

          Hello and welcome once again to my math blog. What is the difference between ‘knowing’ math and ‘understanding’ math?  This question was mentioned in class briefly however I would like to reflect a little more on exactly what the difference is.   I believe that the most effective and powerful learning comes when a student truly understands the knowledge that is being shared with them.  Unfortunately, based on the way math is taught in ‘classic’ classrooms, the assumption has been that once a student is told how to do something they ‘understand’ how to do it. In my opinion this is a very wrong assumption to make. Knowing that the power button will turn on your computer does not necessarily mean that you know how the electronics in your computer works. This to me is what the difference is between ‘knowing’ and ‘understanding’ something. It’s a superficial/procedural knowledge (i.e knowing that the equation P=4s will give you the perimeter of a square) versus a deeper conceptual understanding (if you are looking for a perimeter you are looking for the length of all four sides of the square :. s+s+s+s or simply 4 X S which is also written as 4S). Check out this video on the difference between knowing and understanding:

 

I think teaching for understanding is an important step in the 21 Century classroom and our students should be encouraged to further their understanding rather than parrot the equations that they see in the classroom. I think some of the math teaching methods that we saw in class this week can be used as a way to teach math for understanding. Math Daily 3 allows students to work on their own to resolve math problems, with another to discuss/share and further their understanding, and later reflect on what they have learned. Math congress is also a method that requires students to resolve math problems through first working by themselves, with a partner then sharing with a larger group. I believe these methods can be used for conceptual understanding because rather than use the tradition teacher-centered method of sharing knowledge it requires students to be their own teachers. In other words, students are put in charge of their own understanding, this can be used to further conceptual understanding because students can be allowed to trial and error, to discover what methods work and to share their discovered understanding with their peers. 

Whitfield, Jordan. (unknown) Work Harder. Retrieved from https://bit.ly/2JSbYal

As educators it’s essential for us to give our students the support and encouragement that they need to use student-centered methods to further expand their conceptual understanding. We should encourage our students to take educational risks and to challenge themselves as this is the best way for them to learn and retain valuable information. One key aspect of this is giving meaningful feedback and praise. Praising effort and hard work rather than student ‘smarts’ is one way of doing this. This encourages students to appreciate the ‘hard questions’ in math because they are no longer seen as a gauge of intelligence but rather as a step in the learning process.

Thank you all for reading and see you all next week!

Week 1 Blog Post

Hello and welcome to my math blog, I hope you all had a great summer and ready to go again in our second year of teacher’s college. My first blog is going to focus mainly on our Module 1 reflection questions, as that is what struck a chord with me this first week. 

I really liked the online module as I believe that the themes and questions made us reflect on the effects of math stereotypes, myths and the way media often portrays math. It’s true that social media and entertainment plays a huge role in young peoples’ lives and, whether they know it or not, has a huge effect on the way they think, what they feel and how they react in various situations in their daily lives. Because of this I believe that it is important for educators to be aware of the messages being shared with youngsters in order for them to address and attempt redirect to student beliefs, behaviors and attitudes. The fact of the matter is social media and entertainment frequently not only disperses myths about math but also reinforces math stereotypes by depicting math in a negative light. The math module brought the movie ‘Good Will Hunting’ to mind; I remember that I loved this movie during my youth and watched it more times than I’d like to admit. The main character in this movie was a math genius that, with little effort, was able to solve complex math equations. I remember a particular line in this movie where he expressly said that the numbers just ‘spoke’ to him.  I didn’t realize it back then but this movie, despite how much I enjoyed it, reinforced many math stereotypes that need to be busted in the classroom.

 Here is a list of just a few:

1)           Math is for boys: the main character was a white Caucasian male drop out who was helping a female university student with her math.

2)           ‘You either get math or you don’t’: the main character just ‘got’ math and was able to solve equations that professors and mathematicians around the world were unable to resolve

3)           Math brain is something you are born with: This movie portrayed math in such a way that viewers are lead to believe that a talent for math is something you are either born with or not. You can’t get better at it.

Watching this movie again as an educator (especially one in a math class) is an absolute nightmare; however, messages like these are everywhere in western society. 

In my opinion, and from some discussions I’ve had with other teacher candidates, there are many ways that this problem can be addressed in the classroom. It can be addressed through the teacher’s attitude and approach to teaching math; in other words, have a growth mindset, be positive, be supportive, be helpful and make math interesting. Let student’s know that making mistakes is normal (even in math) and is even encouraged to help them learn and grow.  Make the classroom an emotionally safe place where students feel comfortable taking academic risks and, when possible, make math as inclusive as possible. What do I mean by that? When possible take the time to point out historical figures (for example) who challenge the ‘expected’ status quo. A good example of this is the movie ‘Hidden figures’ that I also mentioned in my reflection module. This movie is excellent to use in math class as well as in history and social studies because not only does it bust the ‘math is for boys’ myth; but it also shows African American Women who, despite adversity, rise past the social expectations of their time and excel in a place and field where they are mostly unwelcome.  

This first week, for me, was a great way to reflect on influences outside of the classroom that teachers need to take into consideration when attempting to engage students in learning. It also pressed the importance of having and instilling a growth mindset into students.

If you would like to know more about the movie Hidden figures check out the below link: 

Unknown. (2016). Hidden Figures. Retrieved from https://imdb.to/2CY25cC