Pst201f Assignment

 

ASSIGNMENT 02

In general the students enjoyed this assignment because most of the work was new andinteresting to them. Allthe answers can be found in Serra. Wrong answers in the assignmentwere corrected by the assessor.

You must know that when naming an object (polyhedron) or a figure (polygon) you mustdistinguish betweenregular and irregular objects or figures. If you are requested to draw andoctagon you must not draw a regular octagon with eight equal sides, because this is a specialcase. When a regular octagon is asked for, make surethat all eight sides are equal and that thefigure is symmetrical. Indicate by marking the equal sides.

The definition of a prism is :a. It is a solid body (polyhedron) with two congruent and parallel bases.Somemathematicians also say that the other faces are parallelograms. Remember that when anobject has acurved surface, it can not be a prism, e.g. A cylinder is not a prism.b. Euler’s equation says: The number of vertices plus the number of faces equals two morethan the edges for any prism or pyramid.

In question 15 there are six possible nets of a cube. (A regular hexahedron), which agree withthe restrictions inthe question. Build the cube to assist your visualisation abilities. Note: Thereare

36

hexaminoes of which

twelve

are nets of a cube, and of these only

six

are in accordancewith the restrictions in the question.

In question 19 the given cube’s top half is red and the bottom half is blue. Therefore all the netswill containsquares which are half-blue and half-red.

The correct answers for Question 20 are: c, b, b, i, c of k, n, j, m, g, i, l, e, a, k. There are other possibilities also.

Latin prefixes are used to indicate the number of sides or faces.

Mono indicates oneBi – indicates twoTri – indicates threeTetra – indicates four Penta – indicates fiveHexa –indicates sixHepta – indicates sevenOcta – indicates eightNona – indicates nineDeca – indicates tenOdeca –indicates elevenDodeca – indicates twelve etc.Thus we can talk about an octagon, which is a figure with eightsides, or an octahedron, which is anobject with eight faces.7 PST201F/201

2 EXAMINATION GUIDANCE FOR PST201F

Your Examination Question paper is a 2 hour paper, with a mark allocation of 100 marks.You have to answer at atempo of one mark per minute.Your examination paper consists of 4 questions:

Question 1

This question consists of 8 paragraph type questions for 35 marks. This covers chapters 1-5 in your prescribedbook.

Question 2

This question consists of 5 paragraph type questions for 30 marks from chapters 1-5.

Question 3

This question is based on the teaching and learning of fractional forms. You will have to link your knowledge andskills related to teaching and learning to the questions posed here (13 marks).

Question 4

This question is based on the teaching and learning of geometry for 22marks. In order to prepare for this question ask the following: “What must I know before I can teach geometrysuccessfully?” Focuson the Van Hiele thought levels.Total 100 marksTo successfully complete this module, youas a student must know, understand and be able to applythe following concepts and ideas.Study the chapters inthe text book that relates to the assignments as well as the following concepts.1.

In the classroom

1.1 Different teaching and learning approaches for example:i. Transmission of knowledge or show-and-tellapproachii. Problem based educationProblem based teaching and learning consists of two kinds, namelyproblem centredlearning. This is where a non-routine problem is used as the vehicle of learning. Problemsolving – this is the approach most often used in our classrooms.This is where a thought provoking activity or task isused as a vehicle of learning. Make surethat you understand the nature of these problems, activities or tasks.(See page 37)1.2 What is meant by the expression

doing of Mathematics?

Can you link certain verbs with thedoing of mathematics?1.3 We must change our teaching environment. Makesure that you know the six mind shiftsnecessary for the classroom environment.1.4 Define assessment1.5 Whatis meant by integration of assessment into instruction and education?

 

PST201F

Five process standards

 –

Problem solving

o

-Reasoning and proof

o

-Communication

o

-Connection

o

 –

Representation

Six shifts

o

Creating an environment equal opportunity to learn

o

Focusing on balance of conceptual and procedural fluency

o

Active engagement in 5 NCTM standards

o

Using technology to enhance understanding

o

Incorporating multiple assesments aligned with instr. Goals

o

Helping students recognise power of sound reasoning

What does it mean to do mathematics

? Means generating strategies for solving problems, applying those approaches, seeing if they lead to solutions, and checking to see if your answers make sense.

Constructivism

-rooted to Jean Piagets work, learners are not blank slates but rather creators of their own learning. Intergrated networks or cognitive schemas are both the product of constructing knowledge and the tools of which additional knowledge can be constructed. As learning occurs these netowrks can be rearranged, added to, or modified.

Reflective thought

 –

effort to connect existing ideas to new information.People modify their existing schemas to incorporate new information.

 Assimilation

- new idea fits in with prior knowledge, expand current network.

 Accommodation

-

new concept doesn’t fit in,

revamp or replace existing network.

Encourage multiple approaches, build opportunities for reflective thought,build new knowledge from prior knowledge,engage students in productive struggle.

Understanding-

 defined as the measure of the quality and quantity of connections that an idea has with existing ideas.

Relational understanding

-knowing what to do and why.

Instrumental understanding

-doing something without understanding.

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