Importance Of Teaching Reasoning And Proof

Example. Solving equations using reasoning and prior knowledge allow students to develop effective reasoning strategies. Through reasoning students gain confidence and conceptual understanding that help them connect ideas to the real world. Let us say that Roberta had 26 papers in her desk. The teacher gave her some more papers and now she has 104. How many papers did her teacher give her?

Geometry in the early elementary grades can build on children's informal knowledge by giving them appropriate vocabulary and opportunities to practice identifying geometric shapes in the classroom and the real world.

Anghileri, J. (2006). Children's mathematical thinking in the primary years perspectives on children's learning (Repr. 2006. ed.). London: Continuum.

Van de Walle, J, Karp, K. S. & Bay-Williams, J. M. (2015). Elementary and Middle School Mathematics Teaching Developmentally. (9th ed.). England: Pearson Education Limited.

In the article, “13 Rules That Expire,” by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty, the three authors discuss thirteen of the most commonly used tricks, tips, and strategies that do not promote a full understanding of mathematics. Furthermore, this promotion of shortcuts and alternatives that are commonly steering children to misunderstandings as they grow and expand their knowledge in a higher level atmosphere. These strategies are that discussed in the article are taught in elementary and middle school levels. However, once these rules are taught and established they tend to expire around grade seven and up when children start learning complex multistep problems. The overall content of the article is accurate when

Reason abstractly and quantitatively- It’s important that students are able to pause during solving the problem and continue to analyze, reflect and strategize for the solution as needed.

Every day, mathematics is used in our lives. From playing sports or games to cooking, these activities require the use of mathematical concepts. For young children, mathematical learning opportunities are all around them. Knaus (2013) states that ‘Young children are naturally curious and eager to learn about their surroundings and the world they live in’ (pg.1). Children, young and old, and even adults, learn when they explore, play and investigate. By being actively involved, engaging in activities that are rich, meaningful, self-directed and offer problem solving opportunities, children given the chance to make connections with their world experiences (Yelland, Butler & Diezmann, 1999). As an educator of young children,

Teachers play an important role in fostering mathematics skills. In the “play dough” (Appendix A) episode, the educators can push student thinking and place the burden of thought on the student. Strategic questioning can really promote higher order thinking a natural integration between math and play (National Council of Teachers of Mathematics [NCTM], 1999). Questions such as “How can you tell which one is the biggest/smallest? How do you put them in order? Teachers should be encouraged to think about, not only the questions they are asking as children are working but also the frame that sets students off to larger problem solving and mathematical discoveries – measure and compare the lengths and capacities (ACARA, 2016). It is important for teachers to think about the questions that are embedded in the task itself but must also analyse the questions to ensure that children are set on a path to deeper understanding of the concept being taught rather than rote regurgitation – as evident in the play dough experience chosen. When it comes to questioning, educators “need to know when to probe, when to wait for answers and when to reinforce responses and when not ta ask questions” (NCTM, 1999, p.187). As seen in the ‘play dough’ (Appendix A) activity chosen, educators can introduce the mathematical concept of measurement and connect new knowledge with old through the use of effective questioning which crates a “link between actions and the language” (Knaus, 2013,

Sarama, J., & Clements, D. H. (2006). Mathematics in kindergarten. (61 ed., Vol. 5, p. 38). YC Young Children. Retrieved from http://media.proquest.com.ezproxy.apollolibrary.com/media/pq/classic/doc/1129349361/fmt/pi/rep/NONE?hl=&cit:auth=Sarama, Julie;Clements, Douglas

The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).

A classroom with a critical and creative thinking environment provides opportunities for higher-level thinking within authentic and meaningful contexts, complex problem solving, open-ended responses, and cooperation and interaction. Many students see math as right or wrong and they don’t question or explore more. As a future math teacher, I want students to learn to question, be critical, and be creative. I want my future students to feel engage in exploration and investigation. I want to equip my students with higher levels of thinking and engagement and make mathematics more relevant and meaningful.

When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower transformation

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Poor reasoning is described as the failure to recognize the obvious or inability to embrace logical view on a phenomenon. It can also be defined as the spirited attempt to invalidate an argument from an informed perspective or ignorance. The poor reasoning makes people abandon strict logical interpretations and instead make assumptions by their beliefs or advance ideas with no strong basis. This paper uses information from an article written in the Slate magazine on 29 August 2013 to describe poor reasoning. Allison Benedikt wrote the article, and it talks about the importance of taking kids to public schools as opposed to private schools. Its title reads, “If you take your kid to private school, you are a bad person.” The article advances an opinion that public schools are better, and should be considered by parents.

The most basic reason Zaslavsky et al. (2012) cite as to why proofs should be taught in school is because doing so can increase and strengthen student’s abilities to communicate mathematical knowledge. Most students are more than capable of applying formulas and solving the problems presented to them in classes with a little practice. A majority of these students, however, have no clue as to why the methods they are using work, or if they will work with any set of numbers they are presented (Yopp, 2009).