Engaging Children Physically and Mentally: The Power of Math Trails - Research Paper Example

? Article Summaries: Math in Action Engaging Children Physically and Mentally: The Power of Math Trails Summary In “Designing Math Trails for the Elementary School,” Kim Margaret Richardson (2004) discussed the role of math trails in making Math more physically engaging and interesting to students. Richardson (2004) stressed that math trails can accommodate math concepts from preschool to college. Math trails are similar to science trails because teachers use a pre-selected and planned route, where students can learn mathematics in an actual environment. Richardson (2004) also explained the benefits of math trails: 1) They can enhance student participation and engagement because they offer exploration and adventure; 2) They can encourage group and class interaction and communication through sharing and learning mathematics concepts together; 3) They are relatively easy to prepare and cheaper than field trips; and 4) Students can learn and reinforce learned mathematics concepts and find them relevant in everyday life. Richardson (2004) indicated that a teacher can make a trail or he/she can collaborate with others to produce a trail that is flexible enough to adapt to different grade levels. She provided a map of a sample trail, sample instructions, and sample activities. She also recommended ideas on how to get started, how to deepen math learning, and how to use the trail. Analysis The main idea of the article is that math does not have to be done individually and while sitting inside classrooms. Instead, it can and should be done outside too, where students can interact with each other and the school/natural environment. This article is related to course readings that emphasize the renewal on how math should be perceived by teachers and students. Teachers and students should stop seeing math as conjectures, formulas, shapes, and numbers with no social or communication value, but something that can be exciting and relevant to children’s and adults’ everyday lives. Richardson (2004) also emphasized resourcefulness, which math trails promote. Schools do not need to spend an extra dime to add this to the curriculum, although teachers will spend extra time designing and regularly improving it. This article presents feasible suggestions, which can make math teaching more engaging for students and teachers. Many math teachers do want to make math more compelling and relevant for their students and math trails can help them do that. At the same time, like what Richardson (2004) recommended, the class can focus on parts of the trail that are specifically related to the curriculum, textbook, and core standards. Aside from high usability, this article is also related to Common Core Standards, especially “CCSS.Math.Practice.MP1,” “CCSS.Math.Practice.MP2,” and “CCSS.Math.Practice.MP3.” Math trails support CCSS.Math.Practice.MP1 because they open students to the opportunity to resolve hands-on real-life problems. For instance, Richardson (2004) recommended asking questions on brick patterns and colors. This question can be related to asking how many more bricks would be needed if another classroom is made and questions about space and patterns. Follow-through questions in class can help students persevere in further understanding math concepts because of additional practical math applications. In addition, math trails support CCSS.Math.Practice.MP2 because of the decontextualization and contextualization processes included in on-site and classroom follow-through activities. Students can abstract the problem more easily because of the actual materials at hand, instead of just reading about them from a textbook. MP2 says: “Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; and knowing and flexibly using different properties of operations and objects” (Common Core State Standards Initiative, 2012). Students can perform quantitative reasoning, for instance, as they try to apply a brick pattern and composition to other potential scenarios that can have real-life uses and benefits. Aside from supporting MP2, math trails facilitate skills needed in CCSS.Math.Practice.MP3. MP3 states: “Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments,” where “They justify their conclusions, communicate them to others, and respond to the arguments of others” (Common Core State Standards Initiative, 2012). Math trails help students understand math concepts and how they are applied in the real world, so that they can also formulate their conjectures and test them in different cases. At the same time, by working in twos or groups, math trails assist the exchange of math ideas and argumentation. These trails test and hone mathematical analysis and communication, thereby helping children think, not just mathematically, but analytically and critically as well. Reaction I have a favorable response to the article because I believe that math trails present an interesting way of combining math, interaction, communication, and physical activity. These students can appreciate math more, if they learn that math builds things that serve diverse human purposes. I will apply math trails and include them in my instruction, connecting them to many math topics. It will be hard to apply this for schools that have little exposed shapes or structures, but this can depend on the power of imagination. Also, when math trails in schools are not feasible because of the climate or limited surroundings, they can be designed in the community, such as parks and other public buildings. Safety must be ensured, nevertheless, so teachers must prepare for all potential risks of learning outside the classroom. A math trail is a journey of learning practical math, math that students can better appreciate and creatively work on. References Common Core State Standards Initiative. (2012). Standards for mathematical practice. Retrieved from http://www.corestandards.org/Math/Practice Richardson, K.M. (2004). Designing Math trails for the elementary school. Teaching Children Mathematics, 8-14. Intuitive Understanding of Chances: Toward More Complex Math Thinking and Concepts Summary In “Eenie, Meenie, Minie, Moe...Building on Intuitive Notions of Chance,” Jeff Frykholm (2001) explored the ability of young children to understand probability through the concept of chance. Young as they are, they can be exposed to games that make them realize how to make predictions, how some outcomes are more probable than others, and how different possible outcomes can result from certain events. Frykholm (2001) argued that children should learn probability through real-life “chance” experiences. He believed that children have an intuitive understanding of chances, which will help them make sense of probability concepts. He emphasized the importance of starting with the language of probability, such as “less likely” and “more likely.” From here, children can develop their probabilistic thinking by trying to predict the outcomes of particular events. Frykholm (2001) offered two probability games, where young children can learn probabilistic thinking: the peek box and two-dice game. These games allowed children to understand the idea of probability continuum and why some events are more/less certain than others. Analysis Frykholm (2001) presented practical and abstract ideas on how young children learn probability through their everyday experiences, which can be related to classroom math activities. If his kindergarten-level children can practice probability through a simple game, these games can be springboards to probabilistic thinking and learning related math concepts. Furthermore, this article makes explicit connection to NCTM’s Principles and Standards for School Mathematics, where kindergarten levels learn probability in an informal and experiential manner. Activities should be about answering questions on the chances of an event through using the phrases “more likely” and “less likely.” Moreover, this article connects to course experiences, where I realized that children can learn seemingly complex math concepts, only if we scale it down to their language and actual experiences. In other words, we learn from children the best ways to teach them too. Teachers only have to be open to how childhood experiences and activities, as well as interests and concerns, can be used to teach math concepts. The article provides usable experiences as a teacher because of the inspiration that preschool children can learn probability because they are already experiencing it. For instance, they know that if their mother has work, the probability of them going to the park later is lower or less likely. Also, if there is only one ball and there are two sisters, the probability of them getting one each is not possible, and instead, they can share it together. This article is also usable because of the suggested activities. The peek box will be exciting for young children, especially when colorful balls are involved. They can think of and learn the probabilities of colors and offer intelligent guesses on the number of balls inside. This article can be connected to Common Core State Standards, “CCSS.Math.Practice.MP1,” “CCSS.Math.Practice.MP2,” and “CCSS.Math.Practice.MP8.” For “CCSS.Math.Practice.MP1,” Children can make sense of problems of probability through the peek box, for example. A student can write down the color for each peek and determine the range of colors and actual number of balls included in the box. In the article’s example, Kristoffer showed persistence in trying to determine the probability of other colors. He formed conjectures about probabilities based on the data he collected already. The more chances he got peeking into the box, the more satisfied he became that only two colors were in the box. Thus, the activity helped the student learn about the problem and the perseverance needed to solve it. He did not easily give up because he was motivated to answer his own questions about the balls. Learning probabilities in informal games and situations supports CCSS.Math.Practice.MP2 too. In the article’s example, Kristoffer learned how to think about probabilities and outcomes. After every peek event, he slowly changed past conjectures. He updated his ideas based on increasing relevant data. On the one hand, he was decontextualizing the concept of probability through representing it with the right language. On the other hand, he was contextualizing the problem of a third color through analyzing available data. He considered quantities and the chances of the outcomes, which helped understand that the box had most probably two colors only. The article can be related to CCSS.Math.Practice.MP8 too because of how probability games help students find and express consistent reasoning. Kristoffer went through several peeks to understand the probability of a third color. Through his own experiences, he made arguments that soon made him realize that he could not support the argument that a third color existed. Repeated reasoning improved his ability to make logical conjectures. Reaction I have a favorable response for this article because I also know from experience that children use chances and fairness to deal with their daily experiences. Young children may not understand ratios and more complex probabilistic thinking, but the idea of chance can expose them to probability and its continuum. I can use these activities to teach young children how to make predictions, how some outcomes are more likely than others, and how different possible outcomes can result from certain events. Their predictions do not have to be perfect, but at least, they are learning how to express themselves in more precise probabilistic language because they are learning the relevant value of probabilistic thinking. Thanks to this article, math does not have to be purely textbook-based, but something interactive and hands-on. Reference Common Core State Standards Initiative. (2012). Standards for mathematical practice. Retrieved from http://www.corestandards.org/Math/Practice Frykholm, J. (2001). Eenie, meenie, minie, moe...Building on intuitive notions of chance. Teaching Children Mathematics, 112-118. Read More