Number and Operations

984 Words2 Pages
bulb-icon

Recommended: Conclusion for differentiated instruction

Throughout my teaching career I will be required to teach children mathematical skills and concepts in order to help them progress to the next grade. In order to help them master the required standards, I must use different strategies, manipulative devices, models, and technology. Scholarly articles and studies will also be helpful in helping me develop ways to teach my students. In the following paper I will discuss how I would present five different mathematical concepts to my students.

My first concept is comparing relative size of decimals. Students can easily confuse decimal amounts because so many numbers are involved. Students originally learn that more digits equal a greater amount. For example, they might think that 0.2398476 is greater than 0.72 because it has more digits. In order to keep students from being confused and misunderstanding the true amounts, I would teach a strategy called leading digit (Cathcart, Pothier, Vance, & Bezuk, 2011, p. 278). Using the leading digit strategy takes unneeded numbers away making comparing the two fractions easier for the students. The student would keep the first non-zero number and drop the rest of the numbers or replace them with zero. In our example from above, 0.2398476 would become 0.2 and 0.72 would become 0.7. Students would be able to compare 0.2 and 0.7 much easier.

Students would use base-ten blocks to prove that 0.7 is greater than 0.2 (Cathcart et al., 2011, p. 271). By placing rods and one-cubes on the base-ten block to equal the problem we are doing, students could visually see which was bigger and which was smaller. For extra practice, students could work on the following website: http://www.ezschool.com/Games/CompareDecimals.html. This website provides a game w...

... middle of paper ...

...agogical content knowledge.” As long as I prepare, I know that I can teach effectively.

References:

(Cathcart, W.G., Pothier, Y.M., Vance, J.H. & Bezuk, S.B. (2011). Learning mathematics in elementary and middle schools. (5th ed.). Upper Saddle River, NJ: Merrill/Prentice Hall.

Myers, P. (May 2007). Why? Why? Why? Future teachers discover mathematical depth. Phi Delta Kappan, 88, 9. p.691(5). Retrieved February 11, 2012, from General OneFile via Gale:

http://find.galegroup.com.ezproxy.lib.uwf.edu/gtx/start.do?userGroupName=pens49866 &prodId=ITOF

Piccolo, D. (Feb 2008). Views of content and pedagogical knowledges for teaching mathematics. School Science and Mathematics, 108, 2. p.46(3). Retrieved February 11, 2012, from General OneFile via Gale:

http://find.galegroup.com.ezproxy.lib.uwf.edu/gtx/start.do?userGroupName=pens49866 &prodId=ITOF

Show More
Related

  • Content Analysis of Student Learning

    1368 Words  | 3 Pages

    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.

    Read More

  • Is Conceptual Critiques Relevant for Psychology?

    1463 Words  | 3 Pages

    Siegel, L. (1982). The development of quantiy concepts: Perceptual and linguistic factors. Children's logical and mathematical cognition , 123-155.

    Read More

  • Nt1310 Unit 4 Assignment 1

    676 Words  | 2 Pages

    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

    Read More

  • Nt1310 Unit 1 Assignment 1

    1987 Words  | 4 Pages

    Numeracy is a mathematical skill that is needed to be a confident teacher. This unit of study has allowed students to build their knowledge in the mathematical areas of competency and disposition towards numeracy in mathematics. The six areas of mathematics under the Australian Curriculum that were the focus of this unit were; algebra, number, geometry, measurements, statistics and probability. Covering these components of the curriculum made it evident where more study and knowledge was needed to build confidence in all areas of mathematics. Studying this unit also challenges students to think about how we use numeracy in our everyday lives. Without the knowledge if numeracy, it can make it very challenging to work out may problems that can arise in our day to day activities. The knowledge of numeracy in mathematics I have has strengthened during the duration of this unit. This has been evident in the mathematics support I do with year 9 students at school, as I now have a confident and clear understanding of algebra, number, geometry, measurements, statistics and probability.

    Read More

  • Essay On The Seven Pillars Of Reading Instruction

    1207 Words  | 3 Pages

    Teacher knowledge has always been the basis to an effective learning experience. Without a knowledgeable teacher, students are not able to receive a quality educational experience. This pillar encompasses the influence teachers have on student learning and achievement, possession of research based knowledge, and effective teaching practices. I thrive to be educated and knowledgeable on the information presented to my students. By having a variety of teaching techniques that work and I use often in my classroom, I am able to mold my instruction around student needs and provide efficient and

    Read More

  • Not Just a Number: Critical Numeracy for Adults

    1988 Words  | 4 Pages

    "It is difficult to understand why so many people must struggle with concepts that are actually simpler than most of the ideas they deal with every day. It is far easier to calculate a percentage than it is to drive a car." (Dewdney 1993, p. 1) To many people, the words "math" and "simple" do not belong in the same sentence. Math has such an aura of difficulty around it that even people who are quite competent in other areas of life are not ashamed to admit they can't "do" math. Innumeracy is more socially acceptable and tolerated than illiteracy (Dewdney 1993; Withnall 1995). Rather than discussing specific ways to teach math to adults, this Digest looks at emerging perspectives on numeracy and their social, cultural, and political implications as a context for new ways of thinking about adult numeracy instruction.

    Read More

  • Place Value Misconceptions

    948 Words  | 2 Pages

    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.

    Read More

  • Place Value Papers

    1214 Words  | 3 Pages

    Understanding base ten numbers is one of the most important mathematics topics taught in primary school, and yet it is also one of the most difficult to teach and learn. Base ten blocks are used to teach place value concepts, but in a lot of cases, children often do not perceive the links between numbers, symbols, and models. Research shows that many children have inaccurate or faulty number conceptions, and use rote-learned procedures

    Read More

  • Numeracy Case Study

    1041 Words  | 3 Pages

    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.

    Read More

  • Brian Cambourne: Relationship Between Thinking, Learning And Learning

    1056 Words  | 3 Pages

    The cumulative effect of social, cultural and biological evolution.” 2. “The exponential growth of knowledge and the emergence of the “additive curriculum.” 3. “Theoretical confusion about the relationship between “thinking, learning and knowing.” Cambourne elaborated and explained each of the origins and how teachers can help students learn through these in the best ways possible. For the first one, Brian says that we created scholarly disciples as a way of resolving this tension. We also created continuing exponential growth and expansion of knowledge. We need to emerge the additive curriculum and bring thoughts and ideas together. For the second one, he suggests that coverage is more important than depth and that students must first learn what to think and then how to think. Finally, for the third one, Cambourne states that teachers can help students’ become literate in all subjects if they are willing to teach how learning occurs in their field of skill and knowledge. We need to teach students’ how to decode the disciplines by showing and modeling for them as they are engaged with learning the

    Read More

  • The Importance Of Content Knowledge

    732 Words  | 2 Pages

    “…Content knowledge refers to the body of information that teachers teach and students are expected to learn in a given subject….Content knowledge generally refers to the facts, concepts, theories, and principles that are taught and learned…” (edglossary, August, 2013). In contrast, transfer refers to “the ability to learn in one situation and then to use that learning…in other situations where it is appropriate” (Hunter, 1971, p. 2). Moreover, both content knowledge and teaching for transfer are vital aspects in the learning process; especially when it comes to EL (English Learner) students. Thus, teaching core concepts to apply new skills becomes the ultimate goal for instructors.

    Read More

  • My Philosophy of Mathematics Teaching and Learning

    1307 Words  | 3 Pages

    ...S. and Stepelman, J. (2010). Teaching Secondary Mathematics: Techniques and Enrichment Units. 8th Ed. Merrill Prentice Hall. Upper Saddle River, NJ.

    Read More

  • Teaching Mathematics through Guided Discovery

    1245 Words  | 3 Pages

    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.

    Read More

  • Numeracy Essay

    1596 Words  | 4 Pages

    The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...

    Read More

  • The Importance Of Pedagogical Content Knowledge

    883 Words  | 2 Pages

    “Pedagogical content knowledge is a special combination of content and pedagogy that is uniquely constructed by teachers and thus is the "special" form of an educator’s professional knowing and understanding” (Solis, 2009). This is not a novel idea. Lee Shulman, a teacher education researcher, reintroduced the term as he was interested in improving knowledge on teaching and teaching preparation. It was his belief that only developing broad pedagogical skills was inadequate for preparing content teachers just as was promoting education that stressed simply content knowledge (Solis, 2009). Shulman suggested key elements of pedagogical content knowledge including knowledge of representations of subject matter, understanding of students’ conceptions of the subject and the learning and teaching implications that were associated with the specific subject matter, general pedagogical knowledge which are teaching strategies or techniques. His definition of the knowledge base for teaching encompassed other elements: curriculum knowledge; knowledge of educational contexts, and knowledge of the purposes of education (Shulman, 1986). Without the appropriate teacher preparation, many new teachers feel overwhelmed and leave the profession. In the summary report “No Dream Denied: A Pledge to America’s Children” (2010), Ingersoll analyzed the results of a survey

    Read More

More about Number and Operations

Open Document