“When students are able to connect ideas and concepts to procedures and representations, learning is especially robust. Thus, one of the things we want to talk about in mathematics class is how concepts and relationships among concepts connect to what students already know” (Cohen, 2009).
As I read through the chapters, this specific quote really stuck out to me. In elementary school, I really struggled with mathematics. It never made sense to me, and I never saw the way in which math concepts connect. To me, math was a set of different procedures and algorithms. Nothing actually made sense to me. I know that math was this way for me because nobody really took the time to see if I understood what was going on, let alone, pointed out for me the connective nature of mathematical concepts. For example, I never realized how fractions, percentages, or ratios were all interrelated. Thus, this quote really spoke to me, because, as a future educator, I want to make sure that I really show the connections between different mathematical concepts to my learners. I want to teach mathematics by springing off of learners’ prior knowledge. All learners are going to have prior knowledge on a concept and I believe that my lessons should be differentiated for the different levels of prior knowledge my learners have on a given mathematical concept. In order to work with all my learners’ different levels of prior knowledge, and show connections between concepts, I must provide my learners with higher level tasks that allow for multiple types of representations. Thus, the way my learners work out the problems and describe their reasoning for their answers, the more I will start to understand their mathematical understanding of different concepts and how various concepts connect to other concepts. For those learners who don’t understand as well, I will be able to see what prior knowledge they do hold by how they went about solving the problem or how they justify their reasoning compared to learners who understand the concept. Furthermore, having a higher level task will allow me to differentiate learning for my different learners because I will be able to request those learners who understand the concept to provide another representation. I hope if I am able to really build off of learners prior knowledge and to connect mathematical concepts, my learners will start to understand mathematics as a world of interrelated concepts and start to make sense of math more than I did.
Mallory,
ReplyDeleteI couldn't agree with you more. I almost chose this quote myself because it really relates to me as well. I was always able to make a personal connection to every other subject but math for me was a struggle. No teacher ever took the time to explain to me why learning their lessons were important and how learning it would benefit me. Because of this, I have not only struggled with math for a good portion of my formal schooling but I am also unenthusiastic about teaching it myself. I have always told myself that I never what my students to feel how I have felt about math my entire life. I want them to know why this information is important to learn and how they can apply it to their own life. I need to make these personal connections to their own lives as well as to their previous knowledge. I plan to do this but giving examples that will relate to their everyday lives as well as connect to other subject areas. I want to show that math is present everywhere and they can make math apply to so many different areas of interest. I want my students to use what they already know and build upon that. I will work towards showing my students that math is present everywhere and it doesn’t have to be difficult or frustrating.