Week 3!

        This week we touched upon two different concepts that I found interesting, and worth sharing. These two concepts are instrumental understanding, and relational understanding. Instrumental understanding comprehends through steps, such as a formula in math focusing on how to solve a given problem. This is usually only short-term learning, because students are often memorizing formulas but do not understand the actual meaning behind it or how to do something. I can relate to this when I look back to my math classes in high school. Working as a group, or asking the teacher questions just so we could get the assignment done quick and hand it in. No one wanted to sit down and take hours to complete something that could be completed in just under an hour. Also with testing, the teachers usually never gave the formulas to us so I remember having to memorize each one before we had to write a test.
        Whereas, relational understanding is comprehending the concept itself, this includes the “why’s” and “how’s” of the concept. For example, the students know why they are using the specific formula, and how the formula is going to help them solve that problem. This is usually more long-term learning because students can process and understand the information that makes it easier to remember. I think it is extremely important to have a mix of both instrumental and relational understanding incorporated into teachings because students need to be introduced to new things such as a formula, but also need to be taught why they are learning it and how it is beneficial to them in the long run. When I look back I remember associating a formula to a question because it just worked, but never knew why or how it worked. As a future educator, I want to make sure I emphasize relational understanding so students don't look back and think to themselves "I have no idea why I learned that" as I have said previous times in the past.

Lauren. (March 11, 2005). Math Fail. (Online Image). Retrieved from http://bit.ly/2dlKmKB

      This week we also had some fellow teacher candidates present some math lessons focusing on number sense and numeration. One lesson that stuck out to me in particular taught common multiples. In this lesson the teacher candidate had us participate in an activity that allowed students to apply what they have learned in a new way, and what I liked about it the most is that you can use the question more than once by changing the item and cost of the item. The question addressed the prices of new books ($6.00) and used books ($4.00). It then stated that one individual bought all used books, and the other individual bought all new books, however they both spent less than $15.00, but the same amount of money. How many books did each individual buy and what was the total cost? Our teacher candidate presented the information sheet well with little books to represent the used and new ones, as well as a “What we know” box to organize the information that was given. I am a visual learner so I loved this presentation, and would love to use this activity if I ever had to teach common multiples in the future. I also think this is a great example of relational understanding as well because you are taking a math concept and then applying it to a real life scenario that students can relate to. This gives them the idea of how and why were teaching them to understand these concepts.