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Why information communications technologies are important for education
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Analysing understanding is an essay which will discuss the researched issue of Teaching and Learning of ’rate of change (slope)’ in Senior Secondary Schools in Australia. Students require a contextual knowledge of slope “so that they come to see slope as a graphical representation of the relationship between two quantities’ (Center for Algebraic Thinking (CAT), 2014). Without the multiple understandings required to master ‘rate of change’ and algebra many students are ill equipped to go on to levels of higher mathematics. It is necessary to engage students at level where they utilise the skills of enquiry, collaboration, hypothesis, deductive reasoning, and experimentation in real-world examples so that misconceptions are be identified for remedial purposes. The use of Information Communication Technologies (ICT) can greatly assist teachers in providing differentiated learning environments to provide maximum learning outcomes for the diverse student population.
Skemp (1976/2006) defines relational understanding and instrumental understanding and argues the need teachers to adopt relational understanding methods to their teaching practices. Instrumental understanding is simply a remembering of steps or algorithms in a process, which produces correct answers. Relational understanding requires students to gain knowledge, which adds to their schema of the topic being studied, and thereby enables them to apply the correct processes to solve a problem even when confronted with new situations.
The specific curriculum topic that this essay will concentrate on is ‘rate of change’. One problem, not peculiar to mathematics, is that terminology can be confusing to students unless they are schooled in the interpretation of words which are i...
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Skemp, R. (2006). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 12 (2), 88-95. (Originally published in Mathematics Teaching, 77, 20-26, 1976)
Stump, S. L. (2001). High school precalculus students' understanding of slope as measure. School Science and Mathematics, 101(2), 81-89. Retrieved from http://ezproxy.utas.edu.au/login?url=http://search.proquest.com/docview/195206492?accountid=14245
Swan, M. (2009). Improving learning in mathematics. [audio podcast]. Retrieved from https://mymediaservice.utas.edu.au:8443/ess/echo/presentation/a7cee02d-a875-4f39-bf08-2373bb104428/media.mp3
Walter, J. G. & Gerson, H. (2007). Teachers’ personal agency: Making sense of slope through additive structures. Educational Studies in Mathematics, 65(2) pp. 203-233
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.
Variables and Patterns of Change video (Annenberg Media, 2004) follows two teachers, Ms. Green and Ms. Novak, as they begin their school year teaching high school math. Throughout my paper, I plan to show the elements of a non-threatening learning environment as well as the importance of having a non-threatening learning environment. Additionally, I will discuss the similarities and differences between the teacher’s methods in the video. I will explain how the methods are effective and how I would expand on their class lessons.
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
Steen, Lynn Arthur . "Integrating School Science and Mathematics: Fad or Folly?." St. Olaf College. (1999): n. page. Web. 12 Dec. 2013..
I visited Mrs. Cable’s kindergarten classroom at Conewago elementary school one afternoon and observed a math lesson. Mrs. Cable had an attention-grabbing lesson and did many great things in the thirty minutes I observed her. I have my own personal preferences, just like every teacher, and I do have a few things I would do differently. There are also many ways this observation can be related to the material discussed in First Year Seminar.
Reys, R., Lindquist, M. Lambdin, D., Smith, N., and Suydam, M. (2001). Helping Children Learn Mathematics. New York: John Wiley & Sons, Inc.
Brooks, J.G. &Brooks, M.G. (1995). Constructing Knowledge in the Classroom. Retrieved September 13, 2002 for Internet. http://www.sedl.org/scimath/compass/v01n03/1.html.
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).
When conducting this interview, I have learned a lot about the different differentiation strategies that my host teacher uses in her classroom and how they are both similar yet different from tracking students in the classroom. This has informed me on what skills I want to possess in my future classroom and what I want to do to make my students the most successful they can be when learning mathematics.
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.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Teaching young children is possibly one of the most challenging and difficult professions. No matter the subject, an educator must plan, prepare, organize, set up, and review everything that they are going to teach. “Students use mathematics textbooks to study and to do homework questions, while professors and teachers may use them to prepare classes and to teach” (Kajander & Lovric, 2009, p.173). Using textbooks can be a quicker and effective way to help ease the way some educators lesson plan; while teaching without textbooks may be a more difficult task but can be just as rewarding. There are advantages and disadvantages to both, but in the end both can be used in the classroom resulting in similar outcomes. Some of the best educators are
Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
Allowing children to learn mathematics through all facets of development – physical, intellectual, emotional and social - will maximize their exposure to mathematical concepts and problem solving. Additionally, mathematics needs to be integrated into the entire curriculum in a coherent manner that takes into account the relationships and sequences of major mathematical ideas. The curriculum should be developmentally appropriate to the
To help answer these questions or understand the big idea, the teacher needs to understand ...