A. Review What Was Worked on The Day Before, and Previous Days (Strands).

This strengthens fluency and retention. For example:

"Yesterday you learned how to conjugate two verbs. Which verbs, Mr. Faust."

"Etre (to be) and Faire (to do)." "Right."

How do you conjugate etre? Ms. Washington?"

Continue until je, tu, il/elle, nous, vous and ils are listed on the board.

Then review the strategy; e.g., to make "we," use "ons"; to make "you," use "ez."

Have the whole class and individuals repeat until firm. For example:

"Okay, run through the whole thing again for faire.... Great! Once more..."

Then review application or generalization of the strategy; i.e., verbs IN sentences. "Great. Okay, how do you say, 'I am (a man, woman, strong...)'?" Make sure to correct errors (group and individual) by the model, lead, test (repeat until firm), and retest format.

B. Main Business

1. Attention or Focus. Basically, you are getting or sustaining students' attention to you and/or materials.

a. "Okay, everyone. Listen up."

b. "I need y'all to be watching this."

c. "Let's get together on this now."

2. Orientation or Preparation. Next, establish a mental set for what is coming.

a. "You guys have done great on linear functions. Now, we're going to do something even more interesting--namely curvilinear functions."

b. "How is it that ordinarily-decent folks partipate in genocidal movements?"

c. "After this short lesson, I want us all to know the difference between democratic and nondemocratic forms of social organization."

d. "Our task is to..."

e. "We're going to conjugate a new kind of verb--verbs ending in er."

f. "You've gotten good at solving equations with one unkown. That's child's play to y'all. So now we're going to solve equations with two unknowns. For example,..."

g. "We've discussed how societies are formed and how they socialize new members. But societies don't necessarily last. How long did the Golden Age of Athens last? How long did the Roman Republic last? How long did the thousand year Reich last? How long will the United States last? How long did your parents' marriage last?"

3. Model. Show What (Concepts), Why (Propositions), How (Strategies), and How to (Operations). Here, students witness a faultless demonstration of: a) examples and nonexamples of a concept (e.g., democratic vs nondemocratic social forms); b) a proposition, principle, rule, or relationship (e.g., the principles--or "big ideas"--in math and physics; e.g., acceleration and deceleration); c) a strategy (e.g., for solving an equation); d) an operation (e.g., how to solve an equation, how to graph data points; how to read, evaluate, identify areas to improve, and re-write a paragraph).

a. "Okay. Everyone ready?... Watch this." (With commentary on what you are doing.)

b. "First step is, I look at the columns of numbers labeled X and Y. I look at the first row. The row has one value for X and a corresponding value for Y. Second step, I say the value of X--'12.' Third, I look at the graph, along the X [points to the graph] axis, and I count 12 spaces from the zero [points]..."

c. "Listen to this passage from Gibbon's Decline and fall of the Roman Empire.... I'm looking for a variable or concept in this passage that Gibbon suggests fostered the fall of Rome. Here it is. Ordinary citizens lost their sense of stake in the polis and were less willing to be in the armies. Mercenaries did not care for Rome. They cared for cash. And what happens when the cash runs out? Bye bye Rome. So, the strategy is, you look for a proposition in the text that asserts how one variable (in this case, weakening stake in the polis) leads to a condition or a change that is part of the trajectory of the decline of a social grouping (an army with no personal or sentimental stake in preserving the society that hires it. Then you look for other variables that are asserted to foster more changes along the decline trajectory."

d. "Okay, watch me solve this equation. First I.... See how I end up with... (This becomes students' own basis for examining and guiding their work.) Next I.... See how this second step ends with... Third, I..."

Telling students your reasoning while demonstrating an operation is called "conspicuous strategy instruction." It enables students to become independent by using the strategy themselves. Here they can be taking notes. The steps also might be written by a student scribe, who copies and passes out the written strategy. This makes the strategy explicit. Students themselves can use it. Notice that seeing, hearing and writing the strategy requires fluency with the see/write or hear/write learning channels.

4. Lead. This step is guided practice. Students do the task (e.g., define or use a concept, demonstrate or find a proposition, use a strategy, perform an operation) with you. You make sure everyone is getting it right.

a. "Okay, here's another passage from Gibbon. Read it out loud with me. Tell me when you think you've spotted a causal variable... Ms. Rich?... Good! Why did you identify that? What's the strategy?..."

b. "Okay, let's solve this same equation again. Do it with me. [Repeat, and have students repeat, the steps in the strategy as you go along.] Great! Okay, let's do another one."

c. "Okay, let's do it together...."

d. "So, what is the definition of democracy?"... Chorus with students: 'Democracy is a form of social organization in which all members participate in policy decisions...'" (Repeat until firm.)

Correct errors of the group (e.g., someone miss-states a strategy step) or individual by the model, lead, test format. "Okay, watch me again... Now do it (say it) with me.... Now you (say it, do it)."

Repeat until students are firm.

Then do another example--an example that differs in inessential details from previous examples. When skill with one exemplar is firm, then (later lessons) introduce examples that differ in essential details--i.e., requiring that students alter or adapt the strategy. For example, "This problem is different from the others. Notice.... So here we have to add a step..."

5. Test. This step does two things: a) It gives students a chance to practice with less scaffolding or assistance (the principle of "mediated scaffolding"); and b) It enables you to identify how well each student gets it.

a. "Okay. Your turn." (Call on the whole class, on one student, on the back row, etc.) "Women only... If a mathematical relationship involves a constant ratio between change in X and change in Y it is called...?"

b. "Ray, come up here and plot data rows 7 to 12 on the graph up here."

Note: It is important immediately to correct errors. This is done by:

a. Telling. "Linear."

b. Showing or modeling. "Okay, watch. The X and Y values on row 7 are 9 and 36..."

c. Leading, by re-starting or backing up a few steps and trying again, and again, and again.

d. A quick "test." "So, what do we do in step 2?"

Make sure to identify concepts, propositions, strategies or operations--"tool skills" and "learning channels"--that may need more work.

6. A Little More Material. [Working on generalization.] Here, for example, you work on another equation, another verb, another passage containing variables that account for the decline of a civilization.

7. Retest. Immediately give a few more opportunities to respond to the new material. Again, correct errors.

a. "Okay, here are some data on prices of cars and sales of cars. Let's plot these."

b. "Here is a description of the decision making process in a small group..... Is it democratic or nondemocratic?"

C. Review

"Today we.... Here are the main things we learned.... Mr. Graham. What's the rule for making the second person formal in a verb ending with re?" Correct errors and firm as needed.

D. Direct Practice.

Give short practice sessions at the end of class. You can have students work on or with the same concepts, propositions, strategies and/or operations (the principle of "repeating 'till firm") and you can try to help students generalize concepts, propositions, strategies and/ or operations to new material. This practice builds fluency, and strengthens generalization to new material and retention. Examples include using flash cards (SAFMEDs), worksheets (problems), and short essays. Move among students correcting errors as needed. Note weak spots to firm later and strengths to build on.