Mathematics – the study of quantity, form, measurement and arrangement
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100% wanted more of these simulations used in their future education
Objectives
These are simulations designed for year 12 mathematics students and are based on NCEA level2 curriculum and Cambridge International A levels.
- The simulations tests students mathematics knowledge and gets them to use what they have learned in simulated problems.
- When playing the simulations the goal is to answer the randomly generated problems correctly.
- Learned material can be aggregated into bigger “chunks” and then applied holistically to broader problems.
- Hints can be requested, as well as the solution if the student cannot solve the problem first time.
- The simulations assist teachers by providing real time/rapid feedback of student’s performance that shows them what areas the class is having problems with, and which individual students are having trouble with the course.
- The simulations should be done one at a time as the content is covered in class.
- The simulations can be run at home or in the classroom with students working individually or as teams.
- Simulation works well as homework, the teacher can easily check the homework is completed and see where students had trouble.
The simulations are based on the qualifications as shown in the table below.
Mathematics: NCEA Level 2 Achievement Standards
| AS | Description | Sim Title |
|---|---|---|
| 2.1 | Manipulate algebraic expressions and solve equations | Algebra |
| 2.2 | Draw straightforward non-linear graphs | Non-linear graphs |
| 2.3 | Find and use straightforward derivatives and integrals | Differentiation and Integration |
| 2.4 | Use coordinate geometry methods | Coodinate geometry |
| 2.5 | Select a sample and use this to make an inference about the population | Samples |
| 2.6 | Simulate probability situations, and apply the normal distribution | Probability |
| 2.7 | Solve straightforward problems involving arithmetic and geometric sequences | Sequences |
| 2.8 | Solve trigonometry problems requiring modelling of practical situations | Trigonometry |
| 2.9 | Solve straightforward trigonometric equations | Trigonometric equations |
Mathematics: Cambridge International A Levels
| Topic | Sim Title |
|---|---|
| Quadratics: Complete the square Find discriminant Solve quadratic equations Solve linear and quadratic inequalities | Quadratics |
| Functions: Find range of given functions Find fg(x) for given f & g | Functions |
| Coordinate geometry: Given end points- Find length of a line Find gradients Find mid points Find equation of a line | Coordinate geometry |
| Circular measure: Convert radians to and from degrees Find arc length and sector area | Circular measure |
| Trigonometry: Solve trig equations | Trigonometry |
*Note: availability of some simulations based on certain achievement standards are limited due to authoring time constraints. However all simulations will be completed by December 2010.
Coordinate Geometry – 2 short video clip
This 1-minute video will give you an idea of how the mathematics sim works for a part of year 12 coordinate geometry.
And this 1-minute video shows you how a model answer is worked out to show the students how to do this for themselves. Each question has a short video like this to teach the student.
Components of a Sim
A sim consists of a teacher briefing, a student briefing, a video introduction, pre and post tests, the simulation, and use of the platform. Clicking on the active links above gives the resources used in the pilot and below is an image of the math pilot simulation for year 12 coordinate geometry.
Math Pilot Feedback Summary
Students found the simulation above average with helping to learn/revise the topic, they enjoyed learning through simulations more than normal schoolwork, and it added a lot of value to their education. Students found it easy to use and thought the overall the pilot programme was beneficial.
- 100% of wanted more of these simulations used in their future education.
- While the sample was small the test results were dramatic and concluded that, on average, students increased their learning by 206%.
- What was the best thing about this programme? “It gave simple equations and it had explanatory videos” Rebecca Cleave, Year 12, Diocesan
- What was the best thing about this programme? “Able to do lots of the same questions which helped me learn the maths and get into my head” Lisa Pocklington, Year 12, Diocesan
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