0.1 Assessment and assessment support  (Page 8/8)

Use the concept of analytical geometry as your topic and construct a mind map (or metacog) containing all the information (including terminology, definitions, formulae and examples) that you know about the topic of analytical geometry.

Possible questions to ask the learner on completion of their metacog:

• Briefly explain to me what the mathematics topic of analytical geometry entails.
• Identify and explain the distance formula, the derivation and use thereof for me on your metacog.
• How does the calculation of gradient in analytical geometry differ (or not) from the approach used to calculate gradient in working with functions?

A suggested simple rubric for marking a metacog:

10 marks for the questions, which are marked using the following scale:

0 - no attempt or a totally incorrect attempt has been made

1 - a correct attempt was made, but the learner did not get the correct answer

2 - a correct attempt was made and the answer is correct

Investigations

Investigations consist of open-ended questions that initiate and expand thought processes. Acquiring and developing problem-solving skills are an essential part of doing investigations.

It is suggested that 2 – 3 hours be allowed for this task. During the first 30 – 45 minutes learners could be encouraged to talk about the problem, clarify points of confusion, and discuss initial conjectures with others. The final written-up version should be done individually though and should be approximately four pages.

Assessing investigations may include feedback/ presentations from groups or individuals on the results keeping the following in mind:

• following of a logical sequence in solving the problems
• pre-knowledge required to solve the problem
• correct usage of mathematical language and notation
• purposefulness of solution
• quality of the written and oral presentation

Some examples of suggested marking rubrics are included on the next few pages, followed by a selection of topics for possible investigations.

The following guidelines should be provided to learners before they begin an investigation:

General Instructions Provided to Learners

1. You may choose any one of the projects/investigations given (see model question on investigations)
2. You should follow the instructions that accompany each task as these describe the way in which the final product must be presented.
3. You may discuss the problem in groups to clarify issues, but each individual must write-up their own version.
4. Copying from fellow learners will cause the task to be disqualified.
5. Your educator is a resource to you, and though they will not provide you with answers / solutions, they may be approached for hints.

The Presentation

The investigation is to be handed in on the due date, indicated to you by your educator. It should have as a minimum:

• A description of the problem.
• A discussion of the way you set about dealing with the problem.
• A description of the final result with an appropriate justification of its validity.
• Some personal reflections that include mathematical or other lessons learnt, as well as the feelings experienced whilst engaging in the problem.
• The written-up version should be attractively and neatly presented on about four A4 pages.
• Whilst the use of technology is encouraged in the presentation, the mathematical content and processes must remain the major focus.

Below are some examples of possible rubrics to use when marking investigations:

Example 1:

Orals

An oral assessment involves the learner explaining to the class as a whole, a group or the educator his or her understanding of a concept, a problem or answering specific questions. The focus here is on the correct use of mathematical language by the learner and the conciseness and logical progression of their explanation as well as their communication skills.

Orals can be done in a number of ways:

• A learner explains the solution of a homework problem chosen by the educator.
• The educator asks the learner a specific question or set of questions to ascertain that the learner understands, and assesses the learner on their explanation.
• The educator observes a group of learners interacting and assesses the learners on their contributions and explanations within the group.
• A group is given a mark as a whole, according to the answer given to a question by any member of a group.

An example of a marking rubric for an oral:

1 - the learner has understood the question and attempts to answer it

2 - the learner uses correct mathematical language

2 - the explanation of the learner follows a logical progression

2 - the learner’s explanation is concise and accurate

2 - the learner shows an understanding of the concept being explained

1 - the learner demonstrates good communication skills

Maximum mark = 10

An example of a peer-assessment rubric for an oral:

My name: ________________________

Name of person I am assessing: _______________________