Contents 1 Introduction 187 2 Why assess? 190



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Unit Five: Building assessment into teaching and learning


Contents

5.1 Introduction 187

5.1 Introduction 187

5.2 Why assess? 190



5.2 Why assess? 190

The purposes of assessment in outcomes-based education 191

When to assess 194

An example of assessment before instruction 195



1. The learner looks at equal amounts, A and B. He is asked which is more, A or B. The learner states that A and B are the same. 196

2. The appearance of the thing with amount B is distorted. The learner is asked if amounts A and B are the same, or different; (and not the suggestive question ‘Which is more?’) 196

3. If the learner says that the amounts A and B are still the same, distort further. 196

If the learner continues to say A and B are the same, the learner has attained the conservation concept. 197


4. If the learner says amounts A and B are not the same, ask which is more. 197

The learner believes what he or she says; it is the learner’s truth at this stage of his or her development. Reasoning will not persuade the learner differently if he or she has not attained the concept of conservation of this quantity. If this is the case, the learner needs to do more practical work comparing quantities, until the concept is understood. 197

Stage 1: Readiness 201

Stage 2: ‘How much’ 201

5.3 What to assess? 202


5.3 What to assess? 202

Assessing outcomes 202

Assessing for reasoning, understanding, and problem-solving 205

Reflecting on what to assess through the teaching of data-handling 209

5.4 How to assess? 210

5.4 How to assess? 210

The phases of assessment 211

Assessment methods, tools and techniques 213

Methods of assessment 217



1) Takes time to read and understand the work before beginning to complete the task. 220

2) Able to read the data from the table and draw up the tally table. 220

3) Able to find the frequencies using the tally table. 220

4) Able to draw the bar graph using tabled information. 220

5) Bar graph completed with the axes correctly marked and labelled. 220

6) Bar graph given the correct title. 220

7) Able to summarise the information presented and interpret the findings correctly. 220

8) Able to justify or explain work when questioned. 220

Tools for assessment 222

5.5 How to interpret assessment? How to report? 229

5.5 How to interpret assessment? How to report? 229

Three points of reference that can be used in assessment 230

How to report? 233

Self-assessment 237

References 238


References 238






Building Assessment into Teaching and Learning

After working through this unit you should be able to:

  • explain the term assessment

  • identify the four purposes of assessment

  • explain the principles of outcomes-based assessment (OBA)

  • describe the role and purpose of assessment in mathematics

  • implement a variety of types of assessment in assessing your learners' performance in mathematics

  • identify and explain the aspects of mathematics learning you ought to consider when assessing learners

  • reflect on the assessment potential of mathematical tasks used in the teaching of basic data handling concepts

  • select appropriate methods, techniques and tools for assessing a learner's performance in mathematics

  • draw up or design your own assessment tasks and rubrics to be used when assessing a learner's work

  • compare various methods of recording a learner's performance





5.1 Introduction

Assessment occupies a central place in education and especially in the mathematics curriculum. When assessment is done well, it empowers everyone because it:


  • informs learners about what they have learned, what they have still to learn and how best to learn it;

  • informs teachers about how to instruct or teach more effectively;

  • informs parents about how best to support their child's learning.

When done poorly, however, assessment can lead to a misrepresentation of learning outcomes and thereby result in superficial teaching and learning. Thus, assessment should be an integral part of teaching and learning which functions as a quality assurance mechanism to ensure good teaching and learning practice.

The idea that assessment can and should contribute constructively to the curriculum has led to some debate and controversy about the nature, role, importance and the place of assessment in education. One view is that there is a need for new assessment practices to complement more traditional, widely used techniques.

These new assessment practices ought to


  • take into account the current curriculum, content and goals

  • inform teaching initiatives in terms of achieving outcomes

  • comply with national and institutional policies.

Pegg (2002:227) adds an additional component to assessment by arguing that an empirically-based theoretical perspective must be taken into consideration when planning assessment. He further states that assessment issues that are always sensitive to the learner's cognitive development should underpin assessment initiatives. To realise the positive potential of assessment in our classrooms, we need a clear idea of

After reading this unit you will be aware that assessment is more than a set of tests or assignments. Assessment has a purpose and we need to establish the purpose of assessment in order to design an appropriate assessment programme that will enable us to achieve our goals. This unit will elaborate on:

  • how the purpose of assessment has changed in the new curriculum

  • the four main purposes of assessment in an educational system.

We will give an illustration of baseline assessment tests used to establish the readiness of learners to measure items using standard units of measurement.

All of the material in the earlier units of this guide has suggested that teaching in accordance with the NCS will result in learner centred teaching. This style of teaching will assist learners to develop their reasoning skills and their ability to solve mathematical problems both in and out of real contexts. The diverse classes that many teachers have to face will also benefit greatly from learner centred teaching, which will be able to address individual needs where appropriate.

Assessment which is not in line with good teaching methods could undermine the value and benefits of that teaching. It is thus essential that the assessment approach you use should support your teaching methods.

Much of the mathematical content used to illustrate and work with the assessment ideas put forward in this unit will come from LO5 (Data Handling). This will give you the opportunity to think about setting tasks that support sound mathematical teaching. We will look at the difference between assessment methods, techniques, and skills. Most importantly we will show that you must relate the purpose of the assessment with what is being assessed. You need to think about what, how and why you assess, how you interpret the results of the assessment and how you will respond to the learners and engage stakeholders in the process.

The following quotation from Assessing Students: How shall we know them? (Derek Rowntree, 1997, Kogan Page, p.11) will serve as a framework for this unit.


  1. Why assess?

Deciding why assessment is to be carried out; what effects or outcomes it is expected to produce.

  1. What to assess?

Deciding, realising, or otherwise coming to an awareness of what one is looking for, or remarking upon, in the people one is assessing.

  1. How to assess?

Selecting, from among all the means we have at our disposal for learning about people, those that we regard as being most truthful and fair for various sorts of valued knowledge.

  1. How to interpret?

Making sense of the outcomes of whatever observations or measurements of impressions we gather through whatever means we employ; explaining, appreciating, and attaching meaning to the raw ‘events’ of assessment.

  1. How to respond?

Finding appropriate ways of expressing our response to whatever has been assessed and of communicating it to the person concerned (and other people).

Rowntree’s points are very much in line with the RNCS for Mathematics for grades R-9, (DOE 2002:93), which states that

Assessment is a continuous, planned process of gathering information about the performance of learners measured against the Assessment Standards (ASs) of the Learning Outcomes (LOs). It requires clearly defined criteria and a variety of appropriate strategies to enable teachers to give constructive feedback to learners and to report to parents and other interested people.

As this unit unfolds, it will assist you in meaningfully interpreting and applying this RNCS definition of assessment.




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