Chapter Fourteen, Algebraic Thinking, Equations, and Functions, begins with defining the big ideas of algebraic and functional thinking. Each big idea is taught by combining objects and mathematical situations and the connection between the two. Algebraic and Functional thinking are taught as early as Kindergarten, where the teacher connects the mathematical situations to real world problems. Algebra is a broad concept; however, if we look at the number system, patterns, and the mathematical model we can make it explicit and connect it to arithmetic. This chapter highlights three major ways to incorporate arithmetic and algebra in the classroom: number combinations, place-value relationships, and algorithms. In each category, there are subcategories that feature properties. It continues to spotlight how to understand, apply, and use the properties presented. Furthermore, the chapter discussed the variety of patterns and functions. Student who make observations are able to understand patterns. Repeating and Growing patterns are the types of patterns seen in a classroom during mathematics. In addition, within these patterns you’ll see are recursive patterns, …show more content…
For example, a common fallacy is the equal sign. The most commonly used symbol in K – 12 and students have hard time understanding it. Its important for the students to know the equal sign, but also the inequality sign. “These signs are how we mathematically represent quantitative relationships” (Van De Walle, Karp, & Bay-Williams, 2016). If the students don’t understand the purpose of equal and inequality signs, then how will they understand and solve a mathematical model. However, misconceptions can be resolved if student are told or supported by a different kind of thinking. Every student can learn if they’re given the opportunity to really understand what they’re
In this time, most teachers’ brains have been numbed from all of the talk about the thinking process and abstract thinking skills (Ravitch). Students need a lot of knowledge to be able to think critically as they are expected to (Ravitch). We stand on the shoulders of those before us, we did not restart as each generation comes up in the world as we wish it would (Ravitch). What we need to be learning is how to use our brain’s capacity to make generalizations so we can see past our own experiences
Math is everywhere when most people first think of math or the word “Algebra,” they don’t get too excited. Many people say “Math sucks” or , “When are we ever going to use it in our lives.” The fact is math will be used in our lives quite frequently. For example, if we go watch a softball game all it is, is one giant math problem. Softball math can be used in many
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
There are many reasons why Algebra matters in life. One reason that comes to mind is from an early age, your understanding and success in algebra can help build math confidence, notable achievements in high school coursework and college readiness, and more importantly help predict one’s salary earnings on so many levels. As one would know that nearly all sports statistics are produced using algebraic equations. Average points per game are used to determine the Most Valuable Player. Winning percentages are used to determine top rankings. These are calculated with concepts learned in Algebra. Formulas are a part of our lives, whether we drive a car and need to calculate the distance, or need to work out our food volume intake for dieting; algebraic formulas are used every day without us even realizing it.
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
This cycle of obedience and passive acceptance can spill over into other aspects of life where learners conform to beliefs and values without critically evaluating them. Brian Crittenden (1972: 146) speaks about “mis-education” which occurs when the content the teacher presents is a “violation of a ‘critical inquiry”. In other words the teacher presents information is such a way as to exclude any opportunity for enquiry.
This book aims to help people feel more comfortable with math and not be so afraid of it. Marilyn Burns goes through