Appendix D: Assessment and Evaluation - Samples
Sample 1: Applications of Mathematics 10

Topic: Data Tables

Prescribed Learning Outcomes:

Problem Solving

It is expected that students will:

• analyse problems and identify significant elements
• determine that their solutions are correct and reasonable
• clearly communicate a solution to a problem and the process used to solve it
• use appropriate technology to assist in problem solving

Number (Number Concepts)

It is expected that students will:

• analyze the numerical data in a table for trends, patterns and relationships
• use words and algebraic expressions to describe the data and the interrelationships in a table with rows that are related recursively

Unit Focus

The overall goal of the unit was to help students understand how they can use tables to represent data and to use tables to solve real world problems. Assessment required students to demonstrate their ability to create tables that represented data, and processes, that they used to solve problems. In as much as possible, students were assessed in terms of their strategic approach to solving problems as well as their ability use strategies to resolve issues relevant to their project work.

Planning The Unit

To develop the unit, the teacher:

• determined the overall goals of the unit
• identified the related IRP outcomes to be targeted in the unit
• identified the prerequisite knowledge and skills students needed to achieve the targeted outcomes included in this unit, and planned for review
• looked for ways to connect students' learning with other desirable outcomes, including those associated with students' attitudes
• looked for ways to encourage students' understanding of the ways in which practical problems are solved mathematically
• planned a variety of integrated instructional and assessment activities to help students achieve identified outcomes
• determined criteria with which to evaluate students' learning for marking and reporting purposes. Whenever appropriate, the teacher involved the students in setting evaluation criteria.
• developed, with students, a rubric that would be used to mark the unit project and its' presentation. The development of the rubric's criteria was done as early as possible, and with the purpose of promoting students' understanding of the work they were expected to accomplish.

The Unit

Recalling, Reviewing and Extending Relevant Concepts

• To review and evaluate students' understanding of the use of tables in financial situations, students were given a mail order catalogue and assigned the task of spending $1000 on at least 10 different items. Cost was to include taxes, and the students were not to go over $1000 in total spending. Students prepared a table that listed the items, their price, GST, PST, and total cost. The teacher asked students to compare the production of such a table with the production of a spreadsheet.

Peer Assessment - Specific areas, such as the calculation of percentages and the use of formulas, were highlighted as students checked their peers' work on a sample basis. The teacher occasionally asked students to comment on how errors might arise and how to correct them when they did arise.

Assessment Strategies - The teacher assessed the extent of students' development of tables, providing assistance as needed. Particular attention was paid to checking the first few entries to ensure students were able to calculate taxes and complete each row.

Demonstrating How to Create A Spreadsheet

• As students worked through the shopping exercise, the teacher explained how a spreadsheet could be used to produce a dynamic table.
• The teacher also pointed out that buying selections made by the students represented a simple market survey. The teacher then introduced to the class the opening of a store in a mall as a way of meeting the shopping choices as expressed by the class.
• The teacher used an example of the opening of a store to encourage the development of relevant mathematical models.
• The teacher asked students to brainstorm for ideas on what steps a potential business owner could take before they were prepared to actively open a business. These steps, with teacher input, became the basis of a unit project.
• The teacher had students develop a flow chart that showed the steps necessary to produce a business plan, and ensured the steps made practical sense.
• Students brainstormed ideas on the types of information and decisions an entrepreneur might make to determine what to stock in the store, how to set up the store, and how to estimate sales and net and gross profit.
• The teacher developed parameters for the store such as using the shape and size of the classroom to represent the store area. This helped students to determine the theme for their store and to be realistic in terms of the inventory. The teacher told students to assume they had some stock storage space in addition to the area represented by the classroom.
• Students developed inventory lists for the store and estimated the wholesale cost of items by dividing the retail costs by 2. Students determined the number of each item to stock and the price that the store would charge for each item.
• The teacher checked students' tables for accuracy, and frequently asked them to explain their choices.
• Students were asked to develop tables that showed inventories, estimated daily sales, costs such as labour and rent, and estimated gross and net profit.

Self-Assessment - Students were encouraged to reflect on their choices in terms of stores that currently exist. They were asked to explain why customers would go to their store rather than to the competition.

Teacher Review - As students developed spreadsheets that represented process in the development of the simple business plan, the teacher reviewed their work both for accuracy and reasonableness. For example, the labour cost for a staff person working in a computer store could be significantly different than for a person working in a clothing store. Salary rates should represent expertise and be reasonable for the type of work expected.

Peer, Small Group and Teacher Assessment - Students were asked at various development stages to report their concepts in a small group setting. Members of the group were asked to provide feedback to the reporter.

In as much as possible, the teacher created an atmosphere that encouraged students to become engaged with the development of their business. Peer input with regard to marketing, advertising, and the way in which products could be displayed to encourage sales was encouraged as way of replicating market surveys.

The demonstration of students' ability to meet the prescribed outcomes, in individual terms, was encouraged through the students' production of a personalized business plan. While the plans were influenced by peer review and teacher input, each student was assessed and evaluated on their able to explain and replicate the production of the tables/spreadsheets they produced. Evaluations by the teacher were done in such a way that each student was held accountable for the meeting of outcomes, regardless of the amount of group, peer, or teacher input that led to its development.

Using Performance Activities in Instruction

• To help students understand the filling of the cells of a spreadsheet, the teacher allowed students to experiment with various simple applications of spreadsheet. Students were encouraged build spreadsheets to find the final costs of items such as snowboards, cars, CDs, etc. with a view to increasing enthusiasm. Students were asked to demonstrate the use of their spreadsheets. The spreadsheets calculated final costs from price by creating a cell that multiplied a price cell by 1.14. As the spreadsheets became more complicated the teacher asked students to test their viability and encouraged peers to assist in trouble shooting.

Defining The Criteria

Mathematical Thinking

To what extent did students:

• demonstrate an understanding of table interrelationships, students were asked to explain how each row was calculated, and what formula might have been used in the context of a spreadsheet
• Use problem solving elements to trouble shoot the develop of their tables and or spreadsheets

Unit Test

Students were given a business plan created by the teacher. The plan had errors in the form of simple tabular mistakes, formulae errors, and unreasonable estimates. The teacher paid close attention to ensure that students could easily find simple errors and yet more able students might be able to offer quite sophisticated suggestions on how to improve the plan.

The plans themselves were marked on a rubric that was developed by the class near the beginning of the project process. The teacher ensured the rubric represented accurately the intended outcomes.

Self-Assessment

Students' assessment of the business plan and related tables were based on accuracy and presentation. Students were asked to include a statement of predicted hourly earnings for the owner of the store based on their estimates of sales and costs. Clearly most students would either rework their plans if the predicted hourly wage was unreasonable or need explain why they might abandon the business if it was deemed unworkable in its present form.

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Revised: September 2001

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