Rich Tasks

One of the articles that we were responsible for reading this week was on the topic of embedding rich tasks within the curriculum. Jennifer Piggott does an excellent job of describing what a rich task is, as she breaks down why rich tasks are so important to our students growth and development. A memorable quote that really stuck with me from the reading was when Jennifer Piggott stated that “On its own a rich task is not rich - it is only what is made of it that allows it to fulfill its potential.” (Piggott, 2011).  I thought that this quote was extremely important because it is our job as teachers, to create tasks for our students that offer different opportunities to meet the needs and levels of all of our learners. From my understanding about our discussions in class, a rich task could be a task that provides students with multiple ways to approach the task. This is important because offering students different levels of challenges allows them to choose the approach that best suits their level of learning and it also gives them opportunity to take on a more challenging approach, if they feel comfortable and want to broaden their mathematical knowledge. Rich task should also be relative to the students (real life connections), generate discussion and student engagement, and allow for learners to pose their own problems. Although, as we discussed in class, not all rich tasks must incorporate all of these things but it will be highly beneficial for your students to include a number of these approaches in your task.

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            This week Daniel and I successfully completed our first webinar! I must admit that I was very anxious leading up to this. I wasn’t really sure how this would turn out because I am not the most tech savvy person, therefore my biggest concern was making sure that our video, audio, and recording was successful.  Thankfully, we had two laptops with us because one of our laptops decided that it did not want to cooperate with us, right before our webinar began. With a small delay, we got into our webinar and everything came full circle. I really enjoyed this experience and I must say that our group got into some great discussion on differentiated instruction. I think the one thing that I really learned about this experience is the importance of discussion and collaboration. Even though it was myself and Daniel presenting, I feel that because our group was so willing to engage in discussion and collaboratively answer questions, we were both able to learn from the experiences of our peers. This is why I think that it is so important for teachers to promote collaborate and student centered learning in their classrooms, so that they can learn from the experiences of others, bounce ideas off of one another, and gain deeper understandings of mathematical content. I am very interested to try and incorporate webinars somehow in my classroom, as I think it is a unique tool that can be used to promote a differentiated way of learning.

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Parallel Tasks

As a teacher, I think that one of the most important things for us to remember is that the students in our classroom differ in many ways and sometimes this becomes evident in their learning. All of our students need a sufficient amount of time and a variety of different problem solving options to appeal to the divers learning styles that we will see within our classrooms.  When we differentiate instruction for our students we are helping our students achieve their learning potential by providing them with the learning landscapes in which they can identify the type of learning style that is suitable for them. This weeks reading focused on differentiation in mathematics instruction. Within the reading of Capacity Building Series: Differenting Mathematics Instruction, I learned that it is very important to value the diversity of students thinking and implement strategies to differentiate the learning process for all of our students. One of the strategies that were discussed throughout the document was providing students with open-ended tasks. An open-ended task is when a teacher provides their students with a problem or a task that has many different ways that the problem can be approached. This problem that is provided to the students does not have a single correct solution to the problem, so that the students can provide an answer to the solution regardless of their knowledge and experience in mathematics.

In the math mindset modules, we watch a video that discusses the relationship between student’s speed in math and their understanding of mathematical concepts. The video suggests that the most successful students are not those that are really fast and don’t mess up, they are the ones that make mistakes and learn from their mistakes.  I found this to be quite interesting because I know that it is completely true but when I was younger, I always felt like math was a race and if I didn’t finish my work as fast as my classmates, then I was falling behind. I was also always worried to make a mistake in math and I think that the majority of students share the same feeling about mathematics.  This is why it is important for teachers to stress that math is not a race and it is okay to make mistakes. The harder that you work at math and the more that you refine your skills with different strategies will help give you a deeper understanding of mathematical concepts.

 This week I got to experience my first webinar as a participant. It was an excellent learning experience for me as Teresa did a great job in leading our group in discussions and activities based on math inquiry. It was really interesting to see how we can all come together via the internet while we were all in different locations to discuss math. As a teacher, I can see myself using webinars in the classroom with my students and perhaps even with my colleagues for my very own professional development.

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To Memorize or not to Memorize?

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 In class this week, we learned many important concepts, strategies, and messages towards mathematics but I think that one of the most important things that I took away from class was when Pat asked us the question, “is it more important to know/do math or understand it?”. This really got me thinking. It took me back to my elementary and high school years, where I can recall a major emphasis on having to memorize mathematical equations. Memorizing a mathematical equation is great but it is essentially useless if the student doesn’t know how to apply and work through the equation to get their answer. In high school, I remember struggling with this. The math teachers would want us to memorize the equations for upcoming tests, assuming that if we knew the equation, we would know how to work with the equation to solve the problem. The problem with memorization in math is that it is not enough to just memorize an equation because many students that do this will not always be able to figure out how to problem solve because they focused on memorizing an equation instead of practicing their math skills to work through the problem. Memorization in math can be beneficial to some students but not all students are able to learn this way and in my high school experience, I believe that this was one of the things that was discouraging made me feel like I was lost at times. Therefore, I believe that it is better to practice and understand mathematics.

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 In one of the readings for class this week, I found a memorable quote that related to designing a responsive mathematical learning environment in your classroom. The quote states “ Effective teachers know that a wrong answer might indicate unexpected thinking rather than a lack of understanding; equally, a correct answer may be arrived at via faulty thinking” – Anthony, G., & Walshaw, M. (2009). I think that this quote is important because it is not right for us to say that a student does not understand mathematical concepts if they answer a question wrong. This is all part of their learning process and we must also make that student feel rewarded for taking a risk. One way that we can do this is with positive reinforcement, feedback, and attitudes towards math.  The second part of the quote also suggests that teachers should not assume that a student fully understands mathematical concepts just because they arrived at a correct answer, we must make sure that the students are practicing and communicating their understanding to support their knowledge.  

 The final topic that I feel was very important that we discussed in class was the Math Daily 3. Which has a framework to help students develop deep understand and mathematical proficiency by allowing them to select Math by themselves, Math Writing, or Math with someone.  This strategy is great because every student learns in a different way and this allows our students to have a choice in their learning and I truly believe that when students have a choice they will be more likely to enjoy what they’re doing and if we can get our students engaged than they are more likely to develop a love for mathematics. 

The Saga Continues

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Welcome to my math blog! It was a wonderful summer but now its time to put our noses to the grindstone. Our first class back had me reminiscing about my previous experiences with math throughout high school and elementary.  I have always been somewhat fearful of math. To be honest, I’m not sure why I was intimidated by math but I know that many people share this feeling. During my teaching placement, I felt that I could relate to many of my students fears of math because I was once in their shoes many years ago.  I was lucky enough to be able to work with some of these students one on one and share some of my experiences with them. One of the main things that I tried to teach them was to have a growth mindset and not get too discouraged if problems arise that they feel they cannot answer. I told them to never give up and to never be afraid to ask questions because sometimes their questions can generate new ideas that may help them solve their problems.  I think that this was really helpful to my students because it made them aware that not they may not always understand mathematical concepts right away but if they believe that they can do it and they keep trying then they will achieve success.

In class we play a game called “game about squares“ which can be accessed online via: http://gameaboutsquares.com/. I really enjoyed this challenging puzzle game. I think that this game could be a great resource for a teacher to use in the classroom. The game is challenging enough that students will be determined to continue playing to try and reach the highest level. I found that many of us got pretty hooked on this game, as we all tried to get the highest score. Which is why it was important to talk about how we could use a game like this one effectively in our classrooms. As a teacher, you want the students to have fun playing the game and to be immersed in the mathematical concepts but you always want to be able to bring the students back after they have played the game for a limited time. In class, we discussed effective ways to use this game in the classroom and I think that it is important to not have the students play the game too long but perhaps, limit their playing time and then use the game as incentive for them to play at a later time.

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Over the past year, my experience in mathematics has grown a great deal. Last years math class, as well as teaching mathematics in my placement has given me a lot of confidence to go out there and teach this subject area but I know that there is still much room for me to grow and develop my teaching skills. That is one of the main reasons why I am looking forward to the next six weeks in class. I believe that everyday is an opportunity for us to learn something new and I am excited to see the new activities and strategies that we will dive into during our class