I’ve been teaching with a direct instruction math program for almost a decade. In that time, I’ve noticed a debate about what direct instruction looks like in practice. So, I thought I’d share some words about my teaching practice, both for an online class and at home, with my own children.
In Rosenshine’s 2008 “Five Meanings of Direct Instruction,” sponsored by the Center for Innovation and Improvement, he specifically notes Saxon Math (2005) as a “successful direct instruction program.” In my experience, very few people have ever actually used Saxon Math, so let’s take a detailed look at it.
Rosenshine notes that direct instruction includes:
- Begin a lesson with a short review of previous
Saxon 5/4 (3rd edition) embraces this whole-heartedly. Every lesson begins with a fact practice sheet, designed to take no more than 5 minutes.
As you can see, these fact practices are not meant to be hard:
but they are revealing of student fact fluency. My bright child struggled mightily with this part of the lesson, because she didn’t know her facts. It took her about 9 months to go from 45 minutes on this worksheet to 15 minutes.
As well, the mental math is meant to scaffold previous learning. Many people skip these, deeming them unimportant, but as Rosenshine notes, these handful of problems help review previous content.
- Begin a lesson with a short statement of goals.
The title of each lesson is that short statement:
- Present new material in small steps, providing for
student practice after each step.
This is the first day of 5/4, meant for bright 4th graders or average 5th graders. Note how the goal is called out on the left. Vocabulary is clearly defined. Visual illustrations are provided. No assumption is made about whether students have learned the concept of addition. Properties are identified, and multiple worked examples are provided.
This is one of the areas where Saxon excels.
- Give clear and detailed instructions and explanations.
When we review this, we see detailed explanations with the worked example. We have the concrete illustration of the sides of the dice, the text based representation of the concept, and multiple abstract representations. We can also see worked examples of the solutions.
- Provide a high level of active practice for all students.
All students are expected to complete the initial reviews. All students are expected to read the text and follow along with the explanations.
- Ask a large number of questions, check for student understanding, and obtain responses from all students.
Teachers like me can — and I do — pull those examples out and work through them with students. Typically, I use whole class checks for understanding by providing multiple answers and asking students to choose a correct answer. Sometimes, I ask students to choose the correct concept. Then we discuss why the wrong solutions are wrong.
- Guide students during initial practice.
Saxon has a unique design for homework practice. Each new concept has a dozen or so practice problems meant for completion with the teacher as the guide.
- Provide systematic feedback and corrections.
As students complete this work, teachers can check for understanding, and correct misconceptions.
- Provide explicit instruction and practice for seatwork exercises and monitor students during seatwork.
Then, Saxon provides about 30 mixed practice problems. The rest of the assignment may or may not include any problems from that day’s lesson. Instead, the assignment consists of interleaved, interval spaced problems.
This is the part of Saxon that people really hate. It seems boring, to do all that work. And yet, the work means that students are putting in effort–effort means putting it into long term memory. It seems unnecessary to have that much practice on concepts they’ve already been taught. (The small bracketed numbers beside each problem refer back to the lesson where that concept was taught.) This is where the philosophy of Saxon and most math programs differ.
The point of Saxon is not just to teach students math. Instead, the point of Saxon is to teach math to the point of fluency. As I tell my students, I should be able to poke them awake at 3 a.m., ask them how to do long division, divide fractions, or factor a trinomial and they should be able to rattle it off half-asleep. The mixed up problem set practice means that students have strong problem discrimination skills, meaning they can easily identify the appropriate strategies. The point of Saxon is to make math easy by making it hard.
If students have continual practice for needed problem types, then they have time to cement the concepts into their long-term memories. It’s not a frantic flutter to understand it today, because they’ll get more practice later, slowly.
As you can see, the curricula is a tight spiral, constantly shifting students from one concept to another, and then coming back after students have had sufficient practice to add another layer of understanding. You must learn in Saxon, because you will never stop having to solve that type of problem.
Each concept is slowly scaffolded, step by slow step. Nothing is too small to review, nothing is assumed. Everything is taught in excruciating detail and then practiced to fluency. Boring? Maybe. Effective? Absolutely.