Reflection 4

Last week we were introduced to parallel tasks. This week we learned about open tasks and rich tasks. Although parallel tasks can be classified as both an open-ended task and a rich task, I have discovered that there are different characteristics to each type of task.

Rich tasks - why are they rich? 
These types of tasks follow certain criteria that allow for deeper thinking in students. These criteria are as follows:

• Allows for range of student abilities and capabilities to solve. 
• Multiple representations can be used to show student thinking based on learning styles and preferences 
• Involves a story or scenario that engages and interests students 
• Connection to real life examples to get students thinking deeply and allows them to see how mathematics can occur in real life situations 
• Promotes student discussion through questioning 
• Enables the use of all 7 mathematical processes
1. Reasoning and proving
2. Selecting tools and computational strategies
3. Representing
4. Connecting
5. Reflecting
6. Communication
7. Problem Solving 

McEachren, Patricia. (2016, September). Halloween Jack-o-lanterns. 

The problem above is an example of a rich task that my professor presented to us. If you compare it to the criteria above, you can see that it is indeed a rich task. I think these types of problems are great for student engagement and to really challenge students. 

Open tasks - how do they promote learning? 

Christopher Danielson. (2013). Which One Doesn't Belong?
[Graphic]. Retrieved from: http://wodb.ca/

These types of tasks give students options, and the opportunity to validate their choice. There will be different answers, but none of the answers that students give are incorrect if they can explain their approach and the strategies they used to solve the problem. I think that these types of tasks promote learning because they give students a chance to think independently and make a choice for themselves. It gets them thinking about their choice and it is accessible to all since they can choose where they want to start. 

In this image, any one of these items can be the one that doesn't belong. It is up to students to decide which one they think doesn't fit based on shape, colour, font, or font colour. As long as students are able to add to the discussion and explain their reasoning, they have succeeded. However, this particular task is not classified as a rich task, because it is not related to math. This series of tasks (Which one doesn't belong) can be found at this site, which asks students which graph, number, shape, and more don't belong. 

Woolley, E. © 2015

This task is an example of an open task word problem. I asked this question to my colleagues during my webinar session on Differentiated Instruction, which I have included below. This particular task is a better example because it is math oriented. As you can see, my peers chose a variety of numbers to work with to solve their problem, which is exactly what we want our students to do. They have a choice on how difficult they make the problem for themselves, so they can challenge themselves based on their abilities.



These types of tasks will be staples in my Math classroom. Not only will the target student interests to get students engaged in mathematics, but they will also challenge them. The great thing about these types of tasks is that it will challenge my students when they solve them, but they will also challenge me to create the problems.