Journal Summary #1: The Story of Kyle & Fracking: Drilling into Math and Social Justice

Journal Summary #1

Article: The Story of Kyle

-NCTM, Teaching Children Mathematics, February 2015, Vol. 21, No.6 (p. 354-361)

Summary:

            Kyle is a kindergarten student from a low-income family. The article showed that Kyle was successfully able to perform nonverbal math calculation activities but struggled to successfully perform on story problems and number combinations. It’s important that children start linking their understanding of numbers to number symbols/representations and number operations. However, many children, especially many low-income children like Kyle, struggle making these connections. Students need to be making these connections, though, in order to be more mathematically proficient and more successful in the future. Therefore, a number sense intervention program (NSI) was developed. It’s an RTI for kindergarteners who may be at risk of math failure. The whole NSI approach is centered on whole-number concepts specifically the number, number relations, and number operations. NSI focuses on representations of numbers and explicit instruction to help improve children’s number sense specifically with story problems and number combinations (which was what Kyle struggled with). There are 24 lessons about 30 minutes long consisting of fast-paced activities in a game-like format. First, students are introduced to a few numbers at a time (i.e. lesson 1-0, 1, and 2, lesson 2- 3, 4, and 5) and they focus on just these numbers. A cardinality chart is used where one block is added for each number (plus one principle) and after that, a number list is used to show the plus-one principle in a different way. Next, students are introduced to part-part-whole through partner cards, and they practice the problem with a farm scene (story problem). Furthermore, children learn how to count effectively using their fingers (count on one hand and then add using the other). This intervention allowed Kyle to be successful and fluent in his math performance.

My Thoughts/How Useful it would be for a Classroom Teacher:

            I think the NSI intervention program is an excellent tool for teachers to use to help kindergarteners (or even other ages) be more proficient at story problems and number combinations. I believe these young students need to learn math through explicit instruction using manipulatives in order to become more fluent in math. The problem I foresee with this intervention is that it appears to be time consuming (there are a lot of steps). However, although it is time consuming, it may be worth it if the students are truly gaining an understanding of numbers. I found this intervention program really interesting. I believe this step-by-step model allows students to break down and process the numbers. I liked the fact that this process was like building blocks (slowly adding another, slightly more challenging concept); as I believe teaching should be, it seemed to go from more physical to more mental/fluent as well as simple to more complex (i.e. cardinality chart-bricks, then number list-circles, partner cards, farm story problem/fingers). In addition, I think this step-by-step model is helpful for lower-achieving students and/or students with learning disabilities because it is clear, slow, breaks down instruction, and provides visual and oral models. I think this intervention would be useful for teachers in a classroom because it allows students to connect with and understand numbers and link that information to symbolic representations of the numbers. They are not only seeing numbers and pictures, but they are learning to make sense of those numbers and pictures. If teachers use this intervention, I think many students would understand/be more proficient in math, less repetition of concepts would be required from the teacher, and more students would progress in their math skills.

Journal Summary #2

Article: Fracking: Drilling into Math and Social Justice

-NCTM, Mathematics Teaching in the Middle School, February 2015, Vol. 20, No.6 (p. 366-371)

Summary:

            The main goal of the teacher in this article was to help her students create a math model to better understand a community issue. She wanted them to see the value of math and how math can help them better understand societal issues. Through models, students can explore real-life situations and make sense of it. This teacher presented students with a relatable society issue question (Should the community ban fracking, or should individuals take advantage of the money?). After learning background information about fracking through videos and articles, a class list of questions related to fracking was brainstormed. Then, she had each student explore/research one aspect of the issue and create a mathematical model. Next, she had them make a presentation (including the student’s question and answer and describing the math they used).  Many students came across challenges when researching their question (information was not available or their question was too broad) or they struggled creating the mathematical model. On the presentation day, students questioned each other about their models and then completed a written reflection showing what they learned about fracking in math and how it can be applied to the real world. Rather than a step-by-step math problem with lots of teacher guidance, the students were engaged in a rich math experience where they were the ones to make math decisions. They were the investigators and had to use the information they researched to create a math model. Furthermore, they needed to decide what information to include and show what their numbers meant.

My Thoughts/How Useful it would be for a Classroom Teacher:

            My favorite aspect about this article was that it was student-centered. The teacher could have simply provided a worksheet about fracking and percentage problems, but this teacher recognized the importance of increasing student engagement and understanding. This teacher wanted students to use a math model to personally connect with the information to gain a deeper learning experience. After discussing general information about fracking, the remainder of this lesson was pretty much student-oriented. They chose the question to research, created a model, and showed what their model meant. While their models may not have been perfect, I appreciated that the students were the explorers. Plus, I think students find it more meaningful when they are truly physically and mentally involved in their learning process (as opposed to being lectured at or handed a worksheet). I think exploring a social issue through a math model would be useful for teachers in a classroom because it allows students to explore math concepts, understand what their numbers mean, and relate to the world around them. I believe that the more teachers provide opportunities for their students to explore social issues through math, the more they will engage, connect with, and understand their findings at a deeper level.