PST201F/201/1/2012Tutorial Letter 201/1/2012 MATHEMATICS AND MATHEMATICS TEACHING PST201F Semester 1 Department of Teacher Education THIS TUTORIAL LETTER CONTAINS FEEDBACK ON THE ASSIGNMENTS AND EXAMINATION PREPARATION Bar code 2 Contents: 1. Here is the start of the suggested flow diagram: . Consult your text book in order to answer each question. Note that your flow diagram must end with percentages. Your flow diagram can be different from the flow diagrams of other students or from the suggested flow diagram but it can still be correct. Question 11 unfortunately does not make sense and will be discarded and corrected. Question 10C must read: The list is incomplete. 2. The correct answers are: Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 C B C A D D B C D C Question 11 (NOT APPLICABLE) Question 12 D Question 13 C Question 14 D Question 15 D Question 16 B Question 17 B Question 18 C Question 19 D Question 20 C ASSIGNMENT 03 This assignment addresses the teaching and learning of fractional forms. Question 1: A suggested flow diagram is started below. Here are the answers to the questions. Feedback on assignment answers Examination guidance Closing remarks 1 FEEDBACK ON ASSIGNMENT ANSWERS ASSIGNMENT 01 (The sixth and seventh edition of the textbook were used. Note the many “new” ideas and the use of the interesting models to assist your learner to understand the concepts relationally. You may use any of the earlier editions) This assignment contains 20 multiple choice questions. 3. 2 One whole is four-fourths shown here 2. Question 2: 2.3..1 2.5 = 0 1 .1 Area..4 1 1 0 1 1 Note the use of 0.. 12 counters are three-fourths Thus one fourth is 4 counters Thus one whole is four fourths equal to 16 counters Draw 16 counters.2 2. set and length models Many possibilities – the assessor of your assignment will assess your real life problem. 1 and 1 as bench marks. Five-fourths is given 2. . Arrangement: 2. Note that the use on models is not a step in the teaching of fractional forms rather it is used to teach and learn each concept and skill related to fractional forms.3.3 PST201F/201 Development of fraction concepts →→The meaning of fractions ↓ Fraction construction → Building on whole number concepts ↓ Concepts of fractional parts Sharing tasks Fraction languagel Equivalent size of fractions Partitioning . multiply the numerators and then the denominators as shown: x 2.4 2.7 x Note the shading of of .8 = note the relationship with the use of the model.9.01 is presented as: . cm x One Hundredth 2.1 Key: One Tenth One Unit cm Ten Units Hundred Units One unit One tenth One hundredth Thus 2. Answer: = Relationship with alorithm: Algorithm: When two proper fractions are multiplied.6 - Answer 2. 9..364 > 0.11 The assessor of your assignment will assess your real life problem.183 2..2 3.5 PST201F/201 2.2 3.10 as benchmarks. Your own ideas will be assessed • • • • • Use the three model types.3 + + = + + = = + + = Many possibilities. 50.789 2.978 > 1..2 = 1 4 + 20 + 1 = 25 (more possibilities) 2. Let the learners use their own method of calculation.10 Note the use of 0.6 + 20.1 5. 1.879 > 0..3 x 0.. Learners must link the addition of fractions tot he addition of whole numbers (more possibilities) .987 > 0. Learners must understand equivalent fractions and how to use it.94 Question 3: 3. .3 is represented as: 2.1. Learners must understand the addition of like fractions..269 + 0...1 3.9. Arrangement: 9.943 > 1.643 > 1.12. 2. 5 x 0.2 Use the key in 2.12. There are other possibilities also. l. When a regular octagon is asked for. e. You must know that when naming an object (polyhedron) or a figure (polygon) you must distinguish between regular and irregular objects or figures. b. Note: There are 36 hexaminoes of which twelve are nets of a cube. Euler’s equation says: The number of vertices plus the number of faces equals two more than the edges for any prism or pyramid. n. The definition of a prism is : a. All the answers can be found in Serra. which is a figure with eight sides.g. It is a solid body (polyhedron) with two congruent and parallel bases. a. Therefore all the nets will contain squares which are half-blue and half-red. e. Thus we can talk about an octagon. which agree with the restrictions in the question. g. k. which is an object with eight faces. and of these only six are in accordance with the restrictions in the question. (A regular hexahedron).6 ASSIGNMENT 02 In general the students enjoyed this assignment because most of the work was new and interesting to them. Remember that when an object has a curved surface. j. A cylinder is not a prism. b. i. c of k. Some mathematicians also say that the other faces are parallelograms. Latin prefixes are used to indicate the number of sides or faces. Indicate by marking the equal sides. m. In question 19 the given cube’s top half is red and the bottom half is blue. Build the cube to assist your visualisation abilities. b. Mono indicates one Bi – indicates two Tri – indicates three Tetra – indicates four Penta – indicates five Hexa – indicates six Hepta – indicates seven Octa – indicates eight Nona – indicates nine Deca – indicates ten Odeca – indicates eleven Dodeca – indicates twelve etc. In question 15 there are six possible nets of a cube. because this is a special case. it can not be a prism. . i. If you are requested to draw and octagon you must not draw a regular octagon with eight equal sides. make sure that all eight sides are equal and that the figure is symmetrical. Wrong answers in the assignment were corrected by the assessor. The correct answers for Question 20 are: c. or an octahedron. with a mark allocation of 100 marks. activities or tasks. Define assessment What is meant by integration of assessment into instruction and education? Make sure that you know the six mind shifts 1. 1.5 .3 1. You will have to link your knowledge and skills related to teaching and learning to the questions posed here (13 marks). This covers chapters 1-5 in your prescribed book. Study the chapters in the text book that relates to the assignments as well as the following concepts. Total 100 marks To successfully complete this module. namely problem centred learning.1 In the classroom Different teaching and learning approaches for example: i. understand and be able to apply the following concepts and ideas.7 PST201F/201 2 EXAMINATION GUIDANCE FOR PST201F Your Examination Question paper is a 2 hour paper. necessary for the classroom environment. Your examination paper consists of 4 questions: Question 1 This question consists of 8 paragraph type questions for 35 marks. Question 3 This question is based on the teaching and learning of fractional forms. This is where a non-routine problem is used as the vehicle of learning. Problem based education Problem based teaching and learning consists of two kinds. Problem solving – this is the approach most often used in our classrooms. In order to prepare for this question ask the following: “What must I know before I can teach geometry successfully?” Focus on the Van Hiele thought levels.2 1. 1. Question 2 This question consists of 5 paragraph type questions for 30 marks from chapters 1-5. Question 4 This question is based on the teaching and learning of geometry for 22 marks. (See page 37) What is meant by the expression doing of Mathematics? Can you link certain verbs with the doing of mathematics? We must change our teaching environment. You have to answer at a tempo of one mark per minute. Transmission of knowledge or show-and-tell approach ii.4 1. Make sure that you understand the nature of these problems. This is where a thought provoking activity or task is used as a vehicle of learning. you as a student must know. 1 Estimation of answers 3.3 Counting in fractions 3.2 3.2.8 1.1 3. How we learn The most important theory on how we learn is called constructivism.4 3.6 1.g.3 2.9 What must be assessed in Mathematics? What is the purpose of assessment? Explain the use of rubrics/control lists/journals as assessment tools. A teacher has to actively listen to his/her learners. Define understanding.5.2.4 2. 2. 2. Discuss the order in which you will teach the concepts and skills related to fraction forms (from the concept of a fraction to percent) Discuss as an example how you will teach the algorithm for addition of proper fractions e.2 The use of benchmark fractions 3.3 Discuss the three types of models defined for the teaching and learning of fractional forms. . Discuss this lesson type in full. representation forms. What does this mean? The teaching and learning of specific concepts and skills.7 1.2 Define conceptual knowledge and procedural knowledge. 2. Discuss these 2.5 2. Fractional forms 3.8 1. Discuss this theory.5. 3.5. Mathematical concepts can be represented in five different manners. Can you explain the following? 3. What is meant by reflective thought? Problem based teaching and learning takes place in a lesson which consist of three parts.6 Can you explain why one of the guidelines for teaching fractions is to start with real life situations.5 How will you and your learner build the ‘bridges’ between fractions and decimal numbers and between decimal numbers and percentages.2 2.1 2.6 3 Discuss the benefits of relational understanding.1 Define relational and instrumental understanding of mathematical concepts and procedures. 2 4.8 3.7 3.9 PST201F/201 Geometry 3.3 4. One of the learning outcomes of this module is to assist you to reflect on the teaching and learning of Mathematics. reflect on the following: 4. Summarise the work addressed in these guidelines and then make sure that you understand and .5 NOTE We are aware of the fact that you may use different editions of the prescribed book. 4. Do you still think that the show-and-tell approach (transmission of knowledge) is the only and best approach to teach Mathematics? What is your opinion on drill and memorisation of concepts and skills without real understanding? Will you drill and memorise in your classroom when you know that no real understanding exists? 4.10 Can you supply one activity on each of the following thought levels 0. • Exploring what is meant by knowing and doing mathematics • Teaching through problem solving • Planning in a problem-based classroom • Assessment • Fractions. After completing your preparation for the examination. Give reasons for this statement. Discuss the development of geometrical thought (Van Hiele’s thought levels) What are the characteristics of the thought levels of Van Hiele? 3.11 For enrichment try to do all the activities in the chapters on geometry and measurement. Each of the above guidelines are linked to questions and concepts addressed in the examination. decimal numbers and percentages • Geometric thinking and geometric concepts 3 CLOSING REMARKS The purpose of this letter is to guide you to prepare for the examination in such a manner that you can be successful. 1 and 2? 3. You therefore need to study the chapters related to the following: • Teaching Mathematics in the era of the NCTM standards (these standards are directly linked to the South African learning outcomes for Mathematics curriculum and are therefore applicable). Your own thoughts on the teaching and learning of Mathematics.1 4.4 What happens inside the mind of the learner when he or she learns? What must happen in today’s classroom so that the best education can take place? What can you as teacher do to teach Mathematics more successfully? You have now studied many ideas in an excellent textbook on how to teach.9 Some of the learners in the senior phase cannot successfully do the required geometry. 20 6th edition 1-6. 21 7th edition 1-5. I hope that you enjoyed this module and that you learnt new ideas and concepts about teaching and learning of Mathematics. I hope you will be successful in your examinations You may contact me if you experience problems regarding the content of the module. ideas. 15-17. etc. 15-17.za . 20 5th edition 1-5. 20 DR AM DICKER (012) 429 4630 (08:00-15:00) (012) 429 4583 (secretary) (012) 429 4900 (fax) [email protected] know all the concepts. The following table provides a summary of chapters to study with reference to the different editions of the text book 4th edition 1-5. 15-17. To assist our students even more. 16-18.ac. some of the questions that appear in the assignments are also included in the examination paper.