W33K 3

It is WEEK 3 friends! And that means that we are at exactly 50% of reading my blogs for my math learning at teacher's college! Bittersweet.

via GIPHY (Yes, Simon Gibson. We feel the same way about it being Week 3.)

Question: What is another way to express 50%? 

(Have a few, or many minutes to think.
DID YOU KNOW: Time does not determine how good you are at math!)

Answer: We can express 50% several ways. One way is by fractions: 50/100, and when we find the lowest common denominator, 1/2. We can also call 50% as one-half. Or, we can write it as a decimal: 0.5. We can show this idea visually too, as seen in the image below, with a circle! ↡

Fraction Circle. (2018). Image. Retrieved from https://sites.google.com/a/kcusd.org/5th-grade-fraction-projects/group-2.

Fellow math scholars, there are maaaaany ways to show this concept. You could have shown half of a banana. Or maybe 50% of a pumpkin pie you ate, or half of a pumpkin spiced beverage you drank! There is NO right answer, because, well, they are ALL right and they are ALL connected.

Now, let's get into an interesting topic and break some more crazy math stereotypes. 

Speed Does Not Determine A Student's Ability To Learn, And Mistakes Are Okay!

There are different speeds at which people learn new things, especially math! Do not feel that if you are a slower learner, you have slower or smaller intellectual capacities. In fact, speed does not determine a student's ability to learn and is only a factor of how they absorb, make sense of and process information. Making mistakes in math is also totally okay and sometimes even necessary. Science shows that when mistakes are made, the brain works hard and that hard work creates new brain connections. This actually make the brain grow! So even if you make a mistake, keep trying, your brain will grow as a result! GROWTH MINDSET!

In this video, a really famous person who was a slower math thinker is revealed, can you guess who?

Differentiated Instruction

This new and important information definitely has implications for teachers that are preparing for diverse learners in their math classrooms, since students' math speeds can vary significantly. Capacity Building Series: Differentiating Mathematics Instruction (2008) states that allowing for the right amount of time, or extra time, during math work should be a part of a teacher's differentiated instruction. 

Because differentiation can be challenging, here are some teaching strategies I have discovered that might be helpful in a math classroom.

Differentiating With Open Ended And Parallel Tasks In The Math Classroom

We talked about math centres last time using the Math Daily 3 approach. Today, we will discuss open-ended questions and parallel tasks. 

What are Open Ended Questions?

Open ended questions are questions that allow students to make a choice about the numbers, ideas and strategies they will use to answer a problem. The question is set up in a way where the students will reach the same "big idea" and curriculum component, although each student will get to make a choice and thus, will have a slightly different answer. Consider this example for Grade 5 Patterning and Algebra below:

Q: "Create and draw a pattern that has two steps (i.e., multiply by 2 and add 3). Then, show 2 different ways to represent your pattern (i.e., numerical, in a table, etc.)". 

The teacher is asking for the same "big idea", but is allowing the student to create their own version of the question. This is good for differentiating because students do not feel trapped by a fixed question and can use the numbers and strategies that are at their level of knowledge and skill. This also gives them a feeling of autonomy.

What are Parallel Tasks?

Parallel tasks are similar to open ended questions and are two or more questions provided by the teacher that meet the same big idea, however, are catered to the different math knowledge levels of the students. Teachers create and then look at the question they have posed to students. Teachers then anticipate where some students might struggle. In the parallel task(s), the question(s) are modified to erase those areas of difficulty in order to meet the needs of different learners and allow them to succeed at the question the teacher would like them to solve.

This week, we created a parallel question/task to this question given to us by our instructor: 

Q: "90 students in a school have gone to at least two other provinces.  If this represented 24% of the students in the school, how many students are in the school?"(Bunz, Rebecca, 2018).

We anticipated a few challenges that students may face within this question.

1. The wording (too wordy, let's reduce the words, or make them even more challenging) &
2. The numbers used (let's use smaller (or larger numbers for high ability students)).

The parallel task we created was to differentiate to the lower ability students, or to English Language Learner (ELL) students, and it was:

Q: "100 students go to the same school. If this represented 50% of the population, how many students, in total, go to the school?"

So essentially, students are working with proportions and percentages, which hits the big idea that the teachers needs to cover in the curriculum! BUT, we used friendlier numbers, that had an obvious relationship with each other (i.e., 50 and 100, as opposed to 90 and 24) and also used less words. (Note: depending on the math abilities with ELLs, the numbers might not have to be changed, just the wording). Teachers could make the components of the question easier, or more challenging to differentiate to all learners in the classroom. Parallel tasks are questions that are usually not open ended, although they could definitely be modified to be a mix of the two types!

To further highlight this differentiation process, here is a link from The Learning Exchange to a great video that explains these two concepts again, provides examples and shows students using these methods in an actual Ontario elementary classroom!

I hope that this week helped you to continue understanding some negative math stereotypes. I also hope that you have some new ideas about differentiating instruction in the math classroom! 

That will be all for this week scholars!

Much love,

Teddy