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Better Practice versus More Practice in Algebra 1: Principles of Secondary Mathematics

Does Algebra 1: Principles of Secondary Mathematics (A1:PSM) include enough practice for students? The answer depends on how you define “enough.” 

Mastery Dictates “Enough”

A1:PSM is designed to help students achieve mastery. 

For many families that have chosen to homeschool, mastery is at the center of that decision. We believe strongly in the concept of mastery. As our own Ethan Demme says, “The mastery approach lets students spend the time they need to build strong foundations so that by the time they get to calculus or organic chemistry or whatever other field of study, they are equipped to learn complex topics.” 

And so with a mastery approach, we feel that if your student has mastered the content, they have had sufficient (aka “enough”) practice.

That being said, we have developed the lesson structure in A1:PSM to provide a flexible amount of practice to fit individual learners.

Mastery is individual.

If students are breezing through the Checkpoints in A1:PSM, they may be able to complete the Mastery Check without completing any practice problems.

Is this likely? No.

But is it possible? Yes (but not probable).

Some topics will “click” with your student, while others may not. In those places where it’s “clicking,” additional practice may be perceived more as a punishment than a development tool.

You know your student. We understand mastery. So if your student can complete a Mastery Check without completing any Practice, you can be confident that they can move on and be successful on the Lesson and Unit Tests and later on the Midterm and Final Exams as those problems are rooted in the problems students encounter in the Practices.

Better Practice versus More Practice

Should practice be quantitative or qualitative? We think it should be qualitative. And our approach in A1:PSM echoes that thinking.

The number of problems in each practice is determined by our curriculum and teaching experts. They base the number of problems on the complexity of the topic and the challenge or amount of work involved in successfully discovering or calculating a solution. Why require a student to complete 20 problems when 10 suffice? We want them to love math!

More important than the number of problems is your student’s ability to successfully persevere through them to discover or calculate the correct solution. The A1:PSM curriculum encourages students from the start to make mistakes. Make mistakes…so that you can learn from them. 

If students need more practice, we believe that there is more value in reworking problems that students have already attempted. Again, that perseverance through a problem that a student didn’t get quite right the first time is an invaluable opportunity for greater understanding. To try a problem, be unsuccessful at first attempt, analyze and recognize where the error occurs, and then rework the problem successfully is brilliant. Not only does this method help students master math content, it teaches them to persevere through all sorts of challenges as they grow and experience new things in higher education or in the workplace.

Is There Enough Practice in A1:PSM?

Still not convinced that there is enough practice in A1:PSM?

Let’s compare A1:PSM to our Legacy Algebra curriculum.

In A1:PSM, every lesson Part A and Part B includes two Practice pages each. That’s four Practice pages per lesson. That is the same number of practice pages found in every lesson of Legacy Algebra 1 (Practice A, B, C, and D).

Each lesson of A1:PSM also includes a Targeted Review page. This is similar to the Systematic Review (or Practice E) page in Legacy Algebra. So again, the same number of practice pages are provided in A1:PSM as found in Legacy.

All that being said, if you are going to compare the two, we’d be remiss in not pointing out the many example problems that are presented in A1:PSM lesson videos, along with the Checkpoint problems that students complete before they even begin a Practice page.

Are you surprised?

If it feels like A1:PSM has less practice than Legacy Algebra 1, problem-for-problem that is probably true. However, there are nearly equal numbers of Practice pages provided in both.

The approach is a bit different:

  • A1:PSM is designed to make the appearance of the number of Practice pages a bit more subtle to the student.
  • Additionally, we are recommending that students do only the amount of practice they need to establish mastery.
  • And finally, we are promoting the value of persevering by reworking missed problems to the correct solution before starting a new set of practice problems.
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