Differentiated Instruction

This week in class we continued learning the different strategies in which we can add numbers. As well as learned various techniques of subtracting and multiplying. The purpose of having multiple ways of doing the same problem is to allow students to explore various paths of arriving at one or few solutions. This goes back to the purpose of differentiated instruction, since we have a range of learners in class, it only makes sense that as teacher we have multiple ways of arriving at a solution.

So what is the purpose of alternative algorithms?

When learning is done instrumentally, a student does not know why they arrived at that solution. As mentioned above, everyone learns in different ways and we should compute a variety of methods in finding a solution. Differentiated instruction creates a safety net that students fall back onto when they feel like they are struggling. This form of instruction also gives our teaching a creative touch, broadening the way we think, and at the same time respecting the various learners in the classroom. Having this method of instruction allows for students to be engaged in class while helping them relate to the problem.

An example of differentiated instruction is “Skip Counting.” This allows students to visualize their adding and subtracting problems by drawing them out a number line. The students break the numbers down in chunks that are easier for them to add or subtract by skipping in small and easy chunks on a number line. However, ground rules need to be established when teaching this method; the number line increases to the right and decreases to the left. As long as students are aware of what they are doing, the bumps illustrated on the number line are up to the student as to whether they correlate proportionately to the amount skipped.

Skip count to add demonstrated in class (Khalid, N © 2016)

We continued to explore open math problem investigating the different ways we could achieve an area of 8 m². This math problem further demonstrated that a good math problem allows students to relate, thus captivating their interest. It gives everyone a chance to start on the problem no matter the learning levels. Another benefit allows for collaborative group work, observing different points of view and reasoning. When students are engaged, they involve themselves and ask supporting questions to understand the problem better. Student engagement and interaction results in reflection, making it easy for students to recollect not only the ‘how,’ but also the ‘why’.

Activity demonstrated by Fellow teacher
candidate: Using missing numbers from 1 - 9
 to solve math equations (Khalid, N © 2016)

Finally we explored math activities demonstrated by fellow teacher candidates. One of which was to use dice to perform various numerical expressions. While at my teaching practicum I saw a similar activity being implemented by my associate teacher. The activity involved students rolling a dice 5 times and recording the numbers that appeared on the dice onto each of the five blanks, with a decimal between the last two blanks. This process was repeated nine additional times. Next a random draw was made to multiply or divide each of the ten trails in blanks by 10 or 100. This activity tested their ability to multiply, divide and round numerical values. Overall as teachers we need to realize that when students are focused and engaged learning manifests itself.