Week Four

This week’s learning was very interesting and allowed us to think outside the box about how to encourage students to think outside the box! After this week’s readings, online module, and class, I have developed a new mindset for teaching that is focused on providing equitable learning for all students.

After this week I have developed the mindset that all students should know they can be math thinkers, problem-solvers, and thrive in their mathematical journey. Despite the math concept, theory, equation, or problem, students should feel confident taking risks and challenging themselves. They should be able to develop and grow, and find the strategies that work for them! I learned that this can be accomplished through providing students with rich tasks. This quick video sums up this thought process:

The speaker explains how students should be enthusiastic and engaged in their math learning, leaders in their learning, and can persevere through tasks. This will help them realize the skills and strategies they have to solve the tasks, and can then see themselves as problem-solvers. An interesting thought is that she says how this will actually help teachers learn from the students as well, and understand their crucial role in leading students through the learning by providing rich tasks.

In class we worked on a rich task and then brainstormed after what made it rich. The task itself was:

                   ·      Never-ending

                   ·      Allowed us to think outside the box

                   ·      Made us active learners

                   ·      Provoked free thought

                   ·      Provided room for multiple strategies

                   ·      Engaging

                   ·      Inclusive

                   ·      Allowed us to rationalize our understanding

                   ·      Motivated conversation

                   ·      Allowed creativity

                   ·      Encouraged multiple perspectives

                   ·      Utilized open-ended questions

These are crucial attributes of a rich task, as often times students see math as simply right and wrong; only having one answer. However, math does not need to be objective; subjectivity in math is extremely beneficial to learning. We also discussed and practiced turning word problems into rich tasks. Some tactics to doing so are:

           1.     Taking away information à leaving room to think outside the box

           2.     Flip the question à all students can participate and understand

           3.     Add a layer to the question à multiple perspectives/strategies

Finally, in class we also discussed how this creates a sense of value for students as learners in the classroom: students are provided more opportunities to succeed; they focus more on the process than the answer; they are often more motivated and confident in participating and challenging themselves; and they are provided opportunities to collaborate with peers.

I believe this is creating an equitable experience for learners by valuing them as individual learners.  

            This thought is supported by RichTasks and Contexts by Jennifer Piggott. Jennifer highlights that rich tasks are accessible to a wide range of learners and offer high opportunities for success and for learners to think for themselves (equitable). Rich tasks also have an intriguing starting point to increase motivation, and allow multiple methods and responses to increase engagement (value individual learners). I have noticed a huge shift from textbook learning, equations, and theory-based learning, to a style of learning that centres around problem-solving. The article What is a Mathematically Rich Task by Steve Hewson, suggests that transitioning mathematics from a collection of memorized procedures and facts into a living, connected whole, allows learners to ‘get inside’ the mathematics, creating an engaging and powerful experience. Once again, this is supported through rich problem-solving tasks.

            After reading Teddy’s blog Week IV she makes a great point that in Teacher’s College we have been learning how to enrich our instruction as teachers within all subjects. She highlights that within math specifically, describing the need to bring in manipulatives, real-life applications, and collaboration. She explains the need to provide math learning that is relevant, current, challenging, collaborative, engaging, fosters deep thinking, and is student orientated. These are great starting points to have in mind when creating or providing math tasks for students, in order to ensure they are rich. What I find really important about her blog post is her emphasis on collaborative learning rather than independent learning. This line of thinking overlaps with the online module we completed this week, that encourages students to make mathematical connections through real-life experience and collaborating with others to discuss strategies and answers. This will give students multiple learning opportunities, not only through their own thinking, but through understanding their peers’ thinking. They can also use this collaborative opportunity to justify their reasoning and think even deeper about their own thought process.

Collaboration further promotes equitable learning.

            Finally, I want to leave you with a great blog post from Laura Chandler’s Teaching Resources called How to Turn a World Problem into a Rich Math Task (Part One). It is a great article with a lot of depth and information. I wish to highlight her idea that word problems don’t necessarily constitute a rich task or inspire deep thinking, analysis, or discussion because the solutions can be straight forward; involving a lot of underlining information and circling the numbers, leading to a straightforward answer. She describes how rich tasks are open-ended, inquiry-based questions, and have multiple answers and understandings. This level of critical thinking is what invites all students to the challenge and supports their learning as they strategize and answer the question in a way that is meaningful to them. She continues the article by providing 5 tips for crafting an awesome math task:

               1.     Start with a visual problem

               2.     Remove key words

               3.     Add extra details and information

               4.     Personalize it and make it real

               5.     Turn it into a multi-step problem

For a more detailed description of each tip, check out Laura’s article! It is definitely worth a read. She also goes on to suggest ways or places to find “Equitable” word problems. J

After writing this blog post, my initial thought still stands:

I believe providing rich math tasks for students, is creating an equitable experience for learners by valuing them as individual learners.