Are final exams even necessary?
Are we even allowed to ask this? Finals week in college and high school is always a stressful time, almost as a right of passage. Do assessments need to be stressful patterns of studying, furiously writing, and waiting for results? No. They really don't. However, we do need to take time to celebrate a job well done. We don't work hard only to move onto the next task before us. We should reflect on this past school year well. As homeschoolers, we don't discover if our child knows the material in the algebra text from a final exam. We know from their homework and triads whether they understand the material, but does this negate a final exam? No.
If you'd like to glimpse what your child has explored in the realm of mathematics this year, may I suggest asking an essay question? While combining writing and mathematics may be a nightmare for some students, writing is an essential form of communication. You can also have them give the essay verbally, although a written essay gives them a chance to edit their work and be more thorough. While you can create your own simple or complex essay prompts, here are some prompts that you might want to use:
Pre Algebra: Number sense opens the world of numerical relationships to us. Explain what number sense is and how we use it to make calculations, explore ratios, and describe the world of numbers.
Algebra: Describe a linear relationship. Some things to consider are: what kind of equation defines this kind of relationship, what are some ways to picture this relationship, what happens if I have two of these relationships, how is this different from a quadratic, what worlds are opened to us through these types of relationships, etc.
Algebra 2: Describe a quadratic relationship. Some things to consider are: what terms are used to describe these relationships, how are these relationships explored using different operations, how can we picture this relationship, when is this relationship optimized, what patterns in nature are reflected in these relationships, etc.
Geometry: Triangles and circles have a unique relationship. Explore this relationship by defining, comparing, and analyzing these two shapes.
Trigonometry: Similar triangles lead us into the world of trigonometry, yet are reflected in cyclical patterns in nature. Explain this connection and how triangles have equipped us to understand patterns to the point of predicting the future.
Many students unfamiliar with mathematical essay questions will struggle with these prompts. They are designed for the student to show us what he knows. If you choose to give an essay final exam to your math student, I highly recommend giving her a week to complete the open book assignment. Let's leave the timed tests to the multiple choice CLT.