Teaching Mathematics - Term Paper Example

Big thing Concept Student: Program of Study: Date and Time of Submission Executive Summary History has it that many students enjoy playing games, and through experience we get to learn that games are very productive learning activities. When a teacher considers using games in teaching mathematics educators tries to put a difference between game and activity. The same game needs to have more than one party who then take turns on each of them competing to have a win on his or her side. They both exercise some choice on the directions to take and the movements while playing. The main object that comes out here is the choice of the participants of the game. Activities like that of Ladders or Snakes cannot be classified as a game since winning is fully dependent on chance. The players are not able to make decisions but just to wait and count the number times and rounds the snake goes. Mathematical games are activities are games which involve a challenge against opponents, he further explains that the games are governed by set of rules with clear structures and their finishing points are very distinct. He further argues that mathematical games objectives are specific and cognitive in nature. Part 1 The below concept map is on fractions. The big idea help in driving instructions based on the concept instead of subject specific content. It helps in leading students to look at the content which will help them understand the concept which is learning based on the real world. This implies learning based on the skills and knowledge of the content. This approach help students to become critical thinkers, the ability for students to gain important ability like problem solving among other skills needed in the 21st century. In recent years, the big idea has gained considerable attention as quoted by Hwang et al. (2013) most people uses it in teaching mathematics to gain knowledge of the content and for effective design of the circular. The aim of this paper is to explore what is required if the teacher to help him or her assist students have deeper understanding of the math and its application in day to day real world. Fractions to begin with are used to represent parts of a region, parts of a measure and parts of a set; they can also represent division and ratios. Initially, students experience fractions as parts of a region and parts of a set (Acharya & Sinha, 2015). Later they will be introduced to other meaning of fractions. The structure of fractions consists of the numerator, the value at the top, and the denominator, the value at the bottom. The structure looks more like, There is unification of the components of big idea. For example, six elements connected to big idea was identified by Siemon et al. (2012). They include elements like the count trusting, the value place portioning multiplicative thinking approach among other aspect like proportional reasoning and algebraic generalization reasoning. There is overlapping of these ideas as they are being built alongside each other and normally they do not follow linear pattern. The main concepts within the multiplicative thinking which is built alongside trusting count components and the place value can help in the full understanding of the concepts. It is perceived that students have challenge understanding numbers. Siemon et al. (2012) mentioned that the major distinction in the area of multiplicative thinking is the accessibility of the concept which is not easy for student to understand easily. It takes close to 8 years of understanding. There are three types of fraction; the proper fraction which has a bigger denominator than the numerator for example ⅛, the second is the improper fraction which has a bigger value of the numerator than that in the denominator for example 8/3 and lastly, the mixed fraction which has a whole natural number and a fractional part for example, 1⅔. Operations of fractions. A couple of operations can be done to fractions, like addition, subtraction, multiplication and division. (Multiplication) ½ x ½ = ¼ (division) ½ / 1/2 = 2 (addition) ½ + ½ = 1 (subtraction) ½- ½ = 0. Fraction relationships: they can be changed back and forth into decimals for example, 0.5 -> ½. They also can be simplified or expanded ½-> 2/4 and 3/9 -> 1/3. Fractions can also be equivalent to other fractions like 6/6=5/5=1/1 (Acharya & Sinha, 2015). The development of the fraction as a big idea in the Australian curriculum is progressive throughout to year seven of learning as the first and second year the part-whole of fraction, In the interpretation of the part whole, it should be noted that the denominator gives equal parts in the number whole and shows several of the parts as include in the fraction aspect. The representation of the construct is done with the area model like the shape portioned in equal parts. For example, the area of this triangle has been partitioned into two equal areas. The fraction [Math Processing Error] would refer to 'one part out of two equal parts' of the area of the triangle.   The part-entire utilization of divisions applies in other useful settings including physical amounts, for example, length, volume and gatherings of items. It can likewise be connected to more extract settings, for example, time, as in 'a fourth of 60 minutes' or 'half past five'. The part-entire model offers a supportive prologue to portions (Hurst and Hurrell, 2015). It is additionally valuable for investigating proportionate divisions and the option and subtraction of parts, however there are some potential pitfalls. Parts as units of measure, which is presented in year 3, emphatically associate with the ideas and procedures of direct estimation. Scales are utilized to make direct estimations. When we measure an interim utilizing a ruler, the unit of measure may be centimeters. Every centimeter speaks to a length that is one-hundredth of an entire meter. The estimation from the start of the interim to its endpoint discloses to us what number of units the endpoint is from zero. In the event that we need a more precise estimation we could subdivide the units (centimeters) into littler a balance of (millimeters). Rather than a ruler, think about a number line. The separation in the vicinity of 0 and 1 can be partitioned into equivalent lengths. For instance, the separation can be partitioned into 5 sections to make a unit of measure called one-fifth. Denoting a point on the number line and naming it as [Math Processing Error] implies the fact is a separation of one unit from 0 (Zhang and Sclaroff, 2013). The unit [Math Processing Error] can be separated into littler parts. For instance: isolating [Math Processing Error] into two a balance of makes the new unit of [Math Processing Error]. A portion can be utilized to "work" on an amount. At the end of the day, the part goes about as a capacity (Siemon, Bleckly and Neal, 2012). For instance, to discover 34 of something, a few mixes of operations could happen. You could: Divide by 4, then increase by 3 Multiply by 3, and afterward isolate by 4. The result would be a littler amount than the first amount. For instance, 34× 12 = 9. At the point when a dishonorable division is the administrator, the result will be a bigger amount than the first. For instance, 74× 12 = 21. Operators introduced in year 7 borrow the concept of the preceding fraction studies to conclude the curriculum in Australia (Zhang & Sclaroff, 2013). This can be presented in the table below: Growth and development By the end of Big Idea Indicated Curriculum Links Links to other Mathematics areas Foundation Year Trusting the count In this case the flexible admission for the numbers of the metal object which is based on whole part ten. Subtilizing of the knowledge is derived and accounting like 1, 7 among others are included. Fractions and Decimals - It is distinguished and explained on the two parts which is equal to whole. (ACMNA016). Readily available of the collection of the materials to equal parts which further help in splitting an object into equal parts Number and Place Value The model is recognized and written in numbers and the numbers should be located in the ACMNA013 for easy reference. It help in representing and solving simple addition and subtraction using different approaches and methodology. The rearrangement of parts is done in ACMNA015 Year 2 Place Value Introduction on how place value work and expanding it to large numbers. There is need to improve of these numbers and help the learner to develop capacity to deal with many different ones. Introducing the learner to different shapes including the shape classification and characteristics of different shapes in the object calculation this is done on ACMNA021 A detailed calculation of place value of numbers, addition, subtraction and other mathematical functions of large numbers. Arrangements of these shapes in place value order among other approaches. Year 4 Multiplicative thinking Ability to work adaptably with both the number in each gathering and the quantity of gatherings Ability to work adaptably with both the number in each gathering and the quantity of gatherings Year 6 Multiplicative partitioning Ability to partition quantities and representations equally using multiplicative reasoning (e.g., a fifth is smaller than a quarter, estimate 1 fifth on this basis then halve and halve remaining part again to represent fifths), recognize that partitioning distributes over previous acts of partitioning and that numbers can be divided to create new numbers Fractions and Decimals - Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Number and Place Value recognise, model, represent and order numbers to at least 10 000 (ACMNA052) apply place value to partition, rearrange and regroup numbers to at least 10 0000 to assist calculations and solve problems Year 8 Proportioning Reasoning The introduction of large numbers, fraction and differentiation of higher value numbers to students to help them solve more complex solutions in their daily lives. Expanding on this concept by grouping it different fractions. and representations equally using multiplicative reasoning (e.g., a fifth is smaller than a quarter, estimate 1 fifth on this basis then halve and halve remaining part again to represent fifths), recognize that partitioning distributes over Number and Place Value The model is recognized and written in numbers and the numbers should be located in the ACMNA013 for easy reference. It help in representing and solving simple addition and subtraction using different approaches and methodology. The rearrangement of parts is done in ACMNA015 Year 10 Generalizing Capacity to recognize and represent patterns and relationships in multiple ways including symbolic expressions, devise and apply general rules Fractions and Decimals - Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058 A detailed calculation of place value of numbers, addition, subtraction and other mathematical functions of large numbers. Arrangements of these shapes in place value order among other approaches. Part II: Lesson plan for Algebra It's a term that each educator has heard amid their preparation: separation. Separation is characterized by the Training and Development Agency for Schools as 'the procedure by which contrasts between learners are suited so that all understudies in a gathering have the most ideal possibility of learning' (Zhang and Sclaroff, 2013). This is a lesson anticipate instructing arithmetical for three days. In a huge class, contrasts between understudies may on the substance of it appear to be excessively various, making it impossible to be evaluated, yet separation chips away at 3 key angles which can be summed up as takes after: Readiness to learn Learning needs Interest These distinctions may sound rather expansive, however by applying compelling strategies for separation, it is conceivable to cook for very wide varieties between learners. Master conclusion shifts with regards to a complete rundown of the techniques for separation in the classroom, with some holding that it can fall under upwards of 7 classifications (Acharya and Sinha, 2015). Objective Link with Curriculum The sequence of learning Differentiation Resources & Assessment At the end of this lesson learners should be able to:- Definition and introduction to Biconditionals game 1. The introduction to law of detachment Introduction to the concepts of whole numbers , fractions and other concepts Discussing the concept of algebra of higher order and further concepts, addition, subtraction and more details. Application of algebra in real life situations and how to use it to solve problems. Curriculum area and content Beginnings of three year algebra content Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole) FSiM Key Introducing the learner to different shapes including the shape classification and characteristics of different shapes in the object calculation this is done on. Number and Place Value The model is recognized and written in numbers and the numbers should be located in the ACMNA013 for easy reference. It help in representing and solving simple addition and subtraction using different approaches and methodology. The rearrangement of parts is done in ACMNA015 Increased Students will be required to write number sentences for their algebra. Decreased Students can make use of the algebra wheels to aid their thinking. Resources Smartboard Internet Laptop Algebra pieces or labels Maths notebook Diagnostic Assessment Observations and anecdotal notes on students’ participation with team members Ability to find missing parts of algebra Formative Assessment Ability to complete the wholes successfully A detailed calculation of place value of numbers, addition, subtraction and other mathematical functions of large numbers. Arrangements of these shapes in place value order among other approaches. Advantages of using games and online in teaching Mathematics Acharya & Sinha (2015) argues that before designing a game to use in teaching mathematics the teacher needs to be very careful so that the game designing is not out of the topic desired in the mathematics study, he states that the teacher should ensure that the game matches the objectives of the mathematics. He urges that the number of players to be used during the game to be at the average of four so that students so that the turns come around quickly to a void boredom in waiting and the anxiety amongst the students. The stakes in the game should provide room for an element of chance so that those weak students in the game feel like they also have a chance of winning. The game completion time should be made short so that the students may have that desire of playing the game over and over again because if exploited fully some students will game tired during the process. In order to make the students feel that they are part of the exercise Zhang & Sclaroff (2013) argues that children should be invited to create their own mathematical games or variations of other known games this makes them more excited about the whole exercise. Lin eta al. (2016) States that students need to be actively engaged during lectures and this can only be realized through positive experiences, encouragement, enjoyment a need to get an immediate feedback amongst other factors. Rohan, Gingras & Gruyer (2016) states that students needs to be active in class instead of being passive and this can only be realized when a different a approach of teaching approach like the use of gaming is used especially in mathematics as a teaching model. Better teaching practices encourage lecturers to keep students active by finding mechanisms that help in making them alert through the session (Van de et al., 2013). Hirashima et al., (2015) Argues that some of the advantages of this model of teaching include group debate and participation amongst the students since they will be working together hence encouraging and helping one another because they want to win as a unit. Students are able to enjoy a lot of fun since the level of interaction is very high between them and the teacher. An example of such lecturing through games was introduced in the T game at one of the schools in Australia. The basic game concept used (Hill et al. 2006) developed by management with an aim of developing team work skills and being a race the best team has to win. The game required teams to find the value T by sequence. Figure 1.2 The model requires that for the students to solve B1 they must use A1 and use B1 to solve C1 till the last figure then use H1 to solve A2 then use the same A2 to solve C2 till the last sequence so the students had to work as a team to be able to evaluate and solve the problem presented. Hirashima, et al. (2015) also states that using games to teach mathematics gives the opportunity for building self-concept and gives the students some positive attitude towards mathematics through lowering the level of failure and error. He also states that there is proper interaction between the lecturer and the students when gaming is used. There is also high sense motivation amongst the students since they freely participate and enjoy. Zhang & Sclaroff (2013) also states that since games use a lot of symbols and procedures language barriers amongst students can easily be overcome through this model of learning. The process can’t fail to find its share of challenges. According to Challis (2006) using games in teaching mathematics can be cumbersome and too involving especially to students who are slow in catching up with the game. The other aspect is timing when it is too short some students will not be able to understand the concept within the stipulated time. The process also works with a lot of routine which might be boring to some students According to Australian Association of mathematics for lecturers better train their students in a conducive environment is needed that maximize students learning opportunities, in the last decade new technologies have given teachers more opportunities to approach excellence in teaching. Online teaching provides one of such opportunity through the use of equipment’s like tablets computers and laptops in teaching mathematics. Zhang & Sclaroff (2013) in their technological analysis proposes a way of thinking that has the role of context in the proper integration of technology. Most mathematical courses use symbols and graphs where the teacher literally draws the symbol by hand on the board to explain some concepts in mathematics to the student. The unique concept of online teaching is that it allows users to write symbols and graphics electronically, this gives room to teachers to explore different paths to a given solution or to change his lecturers based on how the audience is reacting (Clark, 2011). Online Teaching of mathematics enables lecturers to respond easily to students questions while keeping records. Online charts are useful for more interactive group discussions between students of distance learning and their tutors (Rohan, Gingras & Gruyer, 2016) Another important feature of online teaching of mathematics is that it enabled the students to watch recording of a session which allowed them to cover for a missed lesson and also revision of concept they had not mastered. A study was carried out in 2007 and 2008 In of the colleges in Australia Pcs were used to carry out most of tutorials They were wirelessly connected to a data projector which allowed the tutor to move around easily in classrooms and give laptops to group of students to write on the screen for many to see (Charles, 2005). It was discovered the writing were easy to read and the students did not have to physically go in front of the class. The model also gave the power of writing to the student rather than the teacher since the students focuses on writing on the screen of the tablet. The research revealed that the method was more understandable and accepted by students since it improved their level of understanding concepts. Online teaching also offered the opportunity of ore research since most materials are online and can easily be captured by the students themselves hence reducing the bulk of work that was left to the tutors (Booker et al., 2014). The study becomes more students oriented and based than tutor based where the tutor had to do everything for the students. The data would be stored for a very long term for references purposes According to Zhang & Sclaroff (2013). This model of teaching did not lack its pit-falls, the cost of acquiring was very expensive to some of the learning institutions and they could just afford the model in its entirety. At times the laptops would not function properly and an expert would be called to check on the machines which was seen as a wastage of time to some students since learning had to stop at some point This method of teaching also brought a lot of laziness to many students since everything was online many did not want to think since they could just download information online. Many students experience had time in writing with the mouse and this slowed the process a beat since the teacher had to make sure that he is at par with everyone so some students took a lot of time to adjust to the new system Conclusion In conclusion teaching mathematics in a very relax and conducive environment is the aim of many teachers most of them want to put a simple concept that is more understandable to students ideas like use of games have benefited students in great deal since it increased their participation due to team work and they could learn easily from each other. Use of online technology like tablets saved a lot of time for the teachers; revisions were made easy for the students those who could not afford to make it classes on time would use recordings to revise. Reference Acharya, A., & Sinha, D. (2015). A weighted concept map approach to generate learning guidance in science courses. In Information systems design and intelligent applications (pp. 143-152). Springer India. Booker, G., Bond, D., Sparrow, L. & Swan, P. (2014). Teaching primary mathematics (5th edition). Frenchs Forest, NSW: Prentice Hall. Chapter 11 (pp. 546-560) Charles, R. (2005). Big ideas and understandings as the foundation for early and middle school mathematics. NCSM Journal of Educational Leadership, 8(1), 9-24. CHARLES NCSM Big Ideas.pdf    Clark, E. (2011). Concepts as organizing frameworks. Encounter, 24(3), 32-44. Retrieved from: www.ojs.great-ideas.org/Encounter/Clark243.pdf  Clarke, D.M., Clarke, D.J., & Sullivan, P. (2012). Important ideas in mathematics: What are they and where do you get them? Australian Primary Mathematics Classroom, 17(3), 13-19. CLARKE ET AL APMC 2012 Big Ideas.pdf   Hirashima, T., Yamasaki, K., Fukuda, H., & Funaoi, H. (2015). Framework of kit-build concept map for automatic diagnosis and its preliminary use. Research and Practice in Technology Enhanced Learning, 10(1), 17.  Hurst, C., & Hurrell, D. (2015). Developing the big ideas of number. International Journal of Educational Studies in Mathematics, 1(1) 1-17. IJESIM_HURST_HURRELL.docx Hwang, G. J., Yang, L. H., & Wang, S. Y. (2013). A concept map-embedded educational computer game for improving students' learning performance in natural science courses. Computers & Education, 69, 121-130. Lin, Y., Shahhosseini, A. M., Badar, M. A., Foster, T., & Dean, J. (2016). A concept map-based cognitive framework for acquiring expert knowledge in industrial environment. In Frontiers in Education Conference (FIE), 2016 IEEE (pp. 1-5). IEEE. Rohani, M., Gingras, D., & Gruyer, D. (2016). A novel approach for improved vehicular positioning using cooperative map matching and dynamic base station DGPS concept. IEEE Transactions on Intelligent Transportation Systems, 17(1), 230-239.  Siemon, D., Bleckly, J., & Neal, D. (2012). Working with the big ideas in number and the Australian Curriculum: Mathematics. In B. Atweh, M. Goos, R. Jorgensen & D. Siemon, (Eds.). Engaging the Australian National Curriculum: Mathematics - Perspectives from the Field. Online publication: Mathematics Education Research Group of Australasia, pp. 19-45. SIEMON ET AL. Big Ideas.pdf     Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally. (8th edition). Boston: Pearson. Chapters 4 and 5 Zhang, J., & Sclaroff, S. (2013). Saliency detection: A boolean map approach. In Proceedings of the IEEE international conference on computer vision (pp. 153-160). Zhang, J., & Sclaroff, S. (2013). Saliency detection: A boolean map approach. In Proceedings of the IEEE international conference on computer vision (pp. 153-160). Read More

Parts as units of measure, which is presented in year 3, emphatically associate with the ideas and procedures of direct estimation. Scales are utilized to make direct estimations. When we measure an interim utilizing a ruler, the unit of measure may be centimeters. Every centimeter speaks to a length that is one-hundredth of an entire meter. The estimation from the start of the interim to its endpoint discloses to us what number of units the endpoint is from zero. In the event that we need a more precise estimation we could subdivide the units (centimeters) into littler a balance of (millimeters).

Rather than a ruler, think about a number line. The separation in the vicinity of 0 and 1 can be partitioned into equivalent lengths. For instance, the separation can be partitioned into 5 sections to make a unit of measure called one-fifth. Denoting a point on the number line and naming it as [Math Processing Error] implies the fact is a separation of one unit from 0 (Zhang and Sclaroff, 2013). The unit [Math Processing Error] can be separated into littler parts. For instance: isolating [Math Processing Error] into two a balance of makes the new unit of [Math Processing Error].

A portion can be utilized to "work" on an amount. At the end of the day, the part goes about as a capacity (Siemon, Bleckly and Neal, 2012). For instance, to discover 34 of something, a few mixes of operations could happen. You could: Divide by 4, then increase by 3 Multiply by 3, and afterward isolate by 4. The result would be a littler amount than the first amount. For instance, 34× 12 = 9. At the point when a dishonorable division is the administrator, the result will be a bigger amount than the first.

For instance, 74× 12 = 21. Operators introduced in year 7 borrow the concept of the preceding fraction studies to conclude the curriculum in Australia (Zhang & Sclaroff, 2013). This can be presented in the table below: Growth and development By the end of Big Idea Indicated Curriculum Links Links to other Mathematics areas Foundation Year Trusting the count In this case the flexible admission for the numbers of the metal object which is based on whole part ten. Subtilizing of the knowledge is derived and accounting like 1, 7 among others are included.

Fractions and Decimals - It is distinguished and explained on the two parts which is equal to whole. (ACMNA016). Readily available of the collection of the materials to equal parts which further help in splitting an object into equal parts Number and Place Value The model is recognized and written in numbers and the numbers should be located in the ACMNA013 for easy reference. It help in representing and solving simple addition and subtraction using different approaches and methodology.

The rearrangement of parts is done in ACMNA015 Year 2 Place Value Introduction on how place value work and expanding it to large numbers. There is need to improve of these numbers and help the learner to develop capacity to deal with many different ones. Introducing the learner to different shapes including the shape classification and characteristics of different shapes in the object calculation this is done on ACMNA021 A detailed calculation of place value of numbers, addition, subtraction and other mathematical functions of large numbers.

Arrangements of these shapes in place value order among other approaches. Year 4 Multiplicative thinking Ability to work adaptably with both the number in each gathering and the quantity of gatherings Ability to work adaptably with both the number in each gathering and the quantity of gatherings Year 6 Multiplicative partitioning Ability to partition quantities and representations equally using multiplicative reasoning (e.g., a fifth is smaller than a quarter, estimate 1 fifth on this basis then halve and halve remaining part again to represent fifths), recognize that partitioning distributes over previous acts of partitioning and that numbers can be divided to create new numbers Fractions and Decimals - Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Number and Place Value recognise, model, represent and order numbers to at least 10 000 (ACMNA052) apply place value to partition, rearrange and regroup numbers to at least 10 0000 to assist calculations and solve problems Year 8 Proportioning Reasoning The introduction of large numbers, fraction and differentiation of higher value numbers to students to help them solve more complex solutions in their daily lives.

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