As we progress through Saxon Math’s lower elementary levels, I fall more in love with the simple process for teaching math it provides. As I have written before, I *need *the help Saxon offers. Not just help: I need a script!

Thankfully, Saxon provides the exact words to say and the exact questions to ask at each stage of each lesson. I marvel at the simple ways it teaches concepts – like fractions and division. I definitely would have benefited from the Saxon methods of incremental development and constant review had I known about it in my elementary years. In fact, I am learning things as I teach my kids that I would love to have known!

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### What Makes Saxon Different?

John Saxon (the author and founder of Saxon Math books) noticed a lack of foundational understanding in his math students. He set out to help remediate the problems by creating simple worksheets for his students. Building on his years of real-world experience as an Air Force engineer and instructor at the Air Force Academy, he constructed a curriculum based on two tenets: incremental development and constant review.

Whereas many math curricula make “mastery” of a concept the goal for each unit, Saxon’s approach is more focused on understanding. This may seem like a distinction without a difference, but I assure you it is not. Mastery approaches to math have a strong tendency to “teach to the test” and make fewer connections between concepts in various strands of math. The result is students who cannot recognize the relationships between their “mastered” facts. Saxon developed a program to help the student almost discover for herself the cords that tie the various math strands together. It is an over all more holistic approach to teaching math.

#### Incremental Development

The first of two constants in Saxon’s math curricula is Incremental Development. Instead of unit-based math study, which offers a unit on fractions, a unit on decimals, etc.; Incremental Development breaks down concepts into simple bite-sized pieces. Each lesson teaches one simple concept. The student is only challenged to attend to one new thing per lesson, which is laid out in the introduction to the lesson.

The concepts stack nicely on top of and next to one another to build a wide base of mathematical understanding. The unit-based approach to math would build small stacks of math knowledge in the same general area, jumping from stack to stack without keeping in mind how the stacks relate to one another. It takes time to build a strong structure such as Saxon’s. Thus, some people believe Saxon to be behind-level in the early years because of this slower and steadier approach.

#### Constant Review

The second constant of Saxon’s math curricula is constant review. Since only one concept is taught per lesson, there is plenty of time for practice on the worksheets. In the early years Saxon also has a timed math facts practice sheet in every lesson.

Although Saxon has been criticized here again – this time for “drill and kill” approach to math facts; his techniques are not without merit. In fact, math facts were the basis for much of math education in the 19th and early 20th century in the early years. However, “new” math approaches have crept in over the last half of the 20th century and early part of this century emphasizing other methods.

Personally, I have come to appreciate the Saxon Math approach to review. I am a firm believer that review is how one cements knowledge into one’s brain. I have also sat back and marveled at how faithful review of math facts over time has increased accuracy and speed in my students.

#### A Word about Timers

Another criticism I hear in regards to math fact review (even and especially from Saxon math users) is the timed math fact sheets. Many, many parent-teachers tell other struggling parent-teachers to disregard the timer and let their students take as long as necessary to complete 20 problems. I must say, I object to this, too.

Both of my current Saxon math students have struggled at some point with the timer. And I am not dictatorial about the timer – we have used other methods to time our math facts practice (fidget spinner races) – but I do *insist* that the math facts practice be a quick process. In response to the occasional complaint from my students, I say:

- These are just to note progress – not perfection. “Even one more today than you got yesterday is a cause for celebration!”
- “You will be surprised at how quickly you can do these!”
- “When you win – and you will – you will be so happy!”

I add more admonishment against grumbling and complaining (Phil. 2:14) if necessary. But my students stopped complaining about the timed math facts when they started getting a sense of success. They started to note their improvement and they were happy!

## Saxon Math + Classical

I don’t honestly know if Saxon would have labeled his approach to Math as Classical. But the Classical method of asking questions to bring out understanding (a.k.a. the Socratic method) is so clearly modeled in Saxon Math. As I work through the lessons with my kids, I see questions, perfectly timed, to spur them to *think* about the answers, to *make connections* to their previous knowledge base, and simply, to *discover* for themselves.

While redeeming my education – teaching my kids through the Classical model – I have often lamented my own lack of knowledge, my own inability to make connections that now seem so obvious. This happens more in our Saxon Math studies than perhaps any other subject. As I am discovering, my math education was woefully inadequate.

Through Saxon’s gentle and steady guidance, students are asked a number of questions. Here are some of the ones I have noticed as I have taught through Saxon 1-3:

- What do you notice?
- What is the strategy for solving these problems?
- Do you see a pattern?
- What kind of story is this?
- How could we find out?
- What did we do ________?

Asking these questions and giving kids the time and *space* to think through the answers is such a wonderful approach to teaching. If this is foreign to the teacher, it can be difficult to walk a student through this process at times. For one thing, it requires patience as the student’s brain begins processing new ideas, figuring out what to do with them.

### Walking a Student through the Saxon Math

Maybe you had an excellent math experience in school. Maybe you never struggled with math concepts or numbers. Man, I wish I was in the same boat. Sadly (and thankfully), I have learned *SO much* in first, second, and third grade math!

No joke! I honestly have learned things I never knew because I was encouraged to observe and *think *like I was never challenged to do in my school days. A recent trip to the craft store’s experience with a clerk leads me to believe I am not alone. For some reason, we have (as a society) become impatient for the time it takes to *think*. We have shielded our kids from that hard thing of thinking so much (in math, handing them calculators and refusing to require memorization of times tables) that cashiers cannot even figure out how to give proper change.

So, if you are like me and are new to this thinking through math thing, may I offer some tips for walking a student through Saxon Math?

**Take the role of lead learner.***you*in the early grades. Soak in the practices your student is learning. Use the Incremental Development Saxon has so expertly offered.**Notice things alongside your student.**Sometimes my student hears a question in a Saxon Math lesson and she simply doesn’t have the vocabulary to answer. Typically, she needs a nudge. After waiting a moment to make sure she is thinking through the process, I offer a follow-up question to clarify or an observation that pushes her in the right direction. Often, my observations are genuine “new” observations; so it is not a put-on for my student. I cannot guarantee some of the observations you will share with your students will be new to you, but I would wager some of them are!**Supplement understanding with math games**(this is one of our favorite books for math games). We have recently just started to do this and I am blown away by how much fun my kids are having as they play math. Play the games alongside your student – they are such a beautiful way to demonstrate you are learning and enjoying “school” as much as they are.**Celebrate the insignificant and the immense.**There is nothing like understanding a concept for the first time! It is exciting! Make sure to share your student’s excitement with him.

Interested in more about Saxon Math? I hope these articles are a blessing to you: