# Laptops In Lessons

Using Internet access devices in Mathematics lessons

## Case Study - Algebra Problems

### Summary

Adapted from material produced by the former Becta organisation - Contains public sector information licensed under the Open Government Licence v1.0.

Ben Clark used a spreadsheet to encourage his students to explore the relationship between the outcomes of different functions and the value given to a common variable.

### Organisational information

Name: Ben Clark
Organisation: Burnt Mill School
Address: First Avenue, Harlow, Essex, CM20 2NR

Located near Harlow town park, Burnt Mill School is an 11-16 mixed comprehensive school of around 1200 students. It is a community school and has specialist status in the Performing Arts (since 2003).

### Project overview

#### What were the aims and objectives of the project?

This activity aimed to develop students' understanding of algebra by exploring the relationship between the outcomes of a series of functions and the value assigned to a common variable. It also encouraged students to use some of the important process skills highlighted in the new curriculum.

#### The activity

Ben's classroom has tables arranged in groups, with four to six students in each group. Groups are given mini-whiteboards to use and they are expected to discuss their ideas.

The activity was structured around an 'algebra puzzle square' of nine cells, each containing numbers. The values of the numbers were determined by nine different functions of the same variable.

As students changed the value of the variable, the outcomes of the functions changed. This created a different set of numbers in the cells of the puzzle square. The puzzle square was constructed by expressing each function as a formula in a simple spreadsheet. The students were only allowed to alter the value of the variable and their task was to identify each of the functions.

Comparing the expressions for individual cells raises questions of equivalence. For instance, is n+20 the same as n*n and therefore can it be the correct solution?

Interesting discussions took place among students as they explored these questions:

• Were the algebraic expressions formulated equivalent even though they appeared to be different?
• What was a suitable value to assign to the variable so that it tested their current conjecture?
• What was the best strategy for solving a task of this type?

Students had to identify the most appropriate values for the variable (that is, smaller numbers are generally easier to deal with than larger numbers). They also had to consider the importance of 0 as the variable and what effect this had in revealing the function (that is, the constant is revealed due to the elimination of any term that includes the variable).

When a group of students believed themselves to have a complete and correct solution, the rest of the class became involved and compared solutions.  Once the class believed they had the correct solution, revealing the formulae in the spreadsheet allowed students to check their accuracy for themselves.

### Barriers and enablers

#### Barriers

Hide the formulae or warn students not to 'click' in the square: unless the spreadsheet is set up so that formulae are hidden, students can see the expression if they 'click' the mouse inside the algebra puzzle square.

#### Enablers

Instant feedback helped students grasp ideas more quickly: using the spreadsheet helped increase the pace of the lesson as students were able to get instant and accurate feedback. This feedback formed the basis of their next attempt, allowing them to develop their mathematics skills.

Minimal ICT skills are needed: students only needed to be familiar with the workings of spreadsheets at an introductory level.

The ICT is flexible: the spreadsheet can be adapted to adjust the level of difficulty and widen the subject content, ensuring that the task meets the needs of the students.

Encouragement is important: some students may need encouragement to write down their expressions on the mini white boards.

### Impact, outcomes and sustainability

The spreadsheet made it easier for the class to cover more ground more quickly. The speedy feedback received by the students meant that they could work at a faster pace in the lesson. Students did many more mental calculations using this activity than if they were doing an exercise from a text book.

Ben argues that his students have benefited from exploring algebraic expressions without really seeing it as 'algebra'.  Students said that they learned to think about the problems, rather than simply memorise rules.

The enthusiasm for this activity has resulted in it becoming a weekly lesson starter. Students have further developed the activity and devised their own spreadsheets and challenges.

### Transferability and portability

Ben was keen to devise an activity that used software that was not subject-specific and was likely to be available in all schools. The activity was written using Microsoft Excel, but could be applied equally to other spreadsheet software packages.  Familiarity with the 'workings' of spreadsheets at an introductory level was all that was required of the user.

The technology also enabled Ben to easily share the resource with members of the department.

### Voice of the learner

The impact of this activity on the students was summed up by one of their comments: "This really makes you think, rather than just learning rules for algebra."

### Conclusion

Spreadsheets are an ideal tool in teaching algebra since students can change the value of different variables and receive instant feedback. Because of this, students do more mental calculations than they would have done using pen and paper.

Minimal ICT skills are required in creating and using the spreadsheet, which makes this activity very easy to replicate.