Countless time teachers encounter students that struggle with mathematical concepts trough elementary grades. Often, the struggle stems from the inability to comprehend the mathematical concept of place value. “Understanding our place value system is an essential foundation for all computations with whole numbers” (Burns, 2010, p. 20). Students that recognize the composition of the numbers have more flexibility in mathematical computation. “Not only does the base-ten system allow us to express arbitrarily large numbers and arbitrarily small numbers, but it also enables us to quickly compare numbers and assess the ballpark size of a number” (Beckmann, 2014a, p. 1). Addressing student misconceptions should be part of every lesson. If a student perpetuates place value misconceptions they will not be able to fully recognize and explain other mathematical ideas. In this paper, I will analyze some misconceptions relating place value and suggest some strategies to help students understand the concept of place value. “Place value understanding requires an integration of new and sometimes difficult to construct the concept of grouping by ten” (Van de Walle, Karp, Bay- Williams, 2013a, p. 193). In the first case study, the student in this problem used a single chip to demonstrate the one in the tens place on his paper. The learner failed to distinguish that the one, stands for a group of ten and not a single chip. This student is still using a count by one approach learned in Kindergarten (Van de Walle, Karp, Bay- Williams, 2013b). The pupil should be exposed to the practice of grouping by ten. The teacher can use a variety of strategies to help the student develop the concept of grouping by ten. To begin, the teacher should encourage the ... ... middle of paper ... ...mathematical concepts is greatly influenced by their understanding of our number system. Consequently, any misconception concerning place value most be addressed promptly in order to ensure success in mathematics. References Beckmann, S. (2014). Mathematics for elementary teachers with activity manual (4th ed.). Boston, MA: Pearson Burns, M. (2010). Snapshots of student misunderstanding. Educational Leadership, 67(5), 18-22. Retrieved from http://web.a.ebscohost.com.ezp.waldenulibrary.org Fuson, K. C., Clements, D. H., & Beckmann, S. (2011). Focus in grade 2: teaching with curriculum focal points. Reston, VA: The National Council of Teachers of Mathematics, Inc. Van de Walle, J.A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication
The lesson is about knowing the concept of place value, and to familiarize first grade students with double digits. The students have a daily routine where they place a straw for each day of school in the one’s bin. After collecting ten straws, they bundle them up and move them to the tens bin. The teacher gives a lecture on place value modeling the daily routine. First, she asks a student her age (6), and adds it to another student’s age (7). Next, she asks a different student how they are going to add them. The students respond that they have to put them on the ten’s side. After, they move a bundle and place them on the ten’s side. When the teacher is done with the lesson, she has the students engage in four different centers, where they get to work in pairs. When the students done at least three of the independent centers, she has a class review. During the review she calls on different students and ask them about their findings, thus determining if the students were able to learn about place value.
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During this lesson, I pushed my students to be able to justify their answers using their knowledge of tens and ones. While not explicitly taught during any of the curriculum lessons, it is a skill required on a number of questions on the test. I predict that some students will struggle with this portion of the test due to their lack of practice using academic language to rationalize their answers. My students “know” what numbers are greater or less, but during this lesson I still heard “I just knew” instead of them going back to their models every time to cite evidence to support their answer. As I finish out this year, and as I think about my teaching practice next year, this is definitely an area of growth that I want to focus
Place value and the base ten number system are two extremely important areas in mathematics. Without an in-depth understanding of these areas students may struggle in later mathematics. Using an effective diagnostic assessment, such as the place value assessment interview, teachers are able to highlight students understanding and misconceptions. By highlighting these areas teachers can form a plan using the many effective tasks and resources available to build a more robust understanding. A one-on-one session with Joe, a Year 5 student, was conducted with the place value assessment interview. From the outlined areas of understanding and misconception a serious of six tutorial lessons were planned. The lessons were designed using
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.
Cook, G., & Cook, J. L. (2010). The world of children. (2nd ed.). Boston, MA: Pearson Education Inc.
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
To supplement the lesson place value worksheets were given out for the students work on at home. Over the course of three days the concept was reviewed at the begging of math class before introducing similar concepts such as adding thousands and ten thousands to the place value work sheets. At the end of the unit the students were given a test that covered
To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses.
Number sense is one of the most important predictors of later mathematical skill (Jo Van Hoof et al., 2017; Geary, Bailey, & Hoard, 2009; Jordan, Glutting, Ramineni, & Watkins, 2010; Mazzocco, Feigenson, & Halberda, 2011). It is used as an umbrella term that includes several different abilities. The term “number sense” not only includes the ability to subitize and count but to compare and estimate quantities, to use derived fact strategy, to link abstract number knowledge with real world quantities, and to switch between different numerical formats based on context and purpose (Berch, 2005; Gersten, Jordan, & Flojo, 2005; Jordan et al., 2007). For example, a study conducted by Dowker (1998) exemplified the different components of number sense
...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.
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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.
Mooney, C.G. (2000). An introduction to Dewey, Montessori, Erickson, Piaget & Vygotsky. St. Paul, MN: Redleaf Press.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school