Procedure

Step 1: Constructing a simple argument (~5 minutes)

Facilitator Notes:

The following exercise focuses on sentence order to help students identify a simple argument structure—background, claim, evidence, justification or linking the evidence with the claim. The exercise also acts as a self-diagnostic in that it will show students where they may experience difficulty or have control over paragraph structure.

• Give students the Correct Order of Sentences – Exercises (PDF, 108 KB) and allow them five minutes to complete the exercise.
• Give or display answer key (PDF, 109 KB) and answer questions about alternative constructions, if there are any.

Step 2: Recognizing a claim (~15 minutes)

• Give students a copy of the Rohrer, Dedrick, Burgess (2014) article (PDF, 387 KB) and instruct them to read the abstract (and only the abstract).
• Students should underline what they believe to be the main claim of the article as expressed in the abstract in one colour.
• Students should underline main pieces of evidence found in the abstract in a different colour.

The following is the abstract with the claims and evidence highlighted.

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use that formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach, different kinds of problems appear in an interleaved order, which requires students to choose the strategy on the basis of the problem itself. In the classroom-based experiment reported here, grade 7 students (n = 140) received blocked or interleaved practice over a nine-week period, followed two weeks later by an unannounced test. The mean test scores were greater for material learned by interleaved practice rather than by blocked practice (72 % vs. 38 %, d = 1.05). This interleaving effect was observed even though the different kinds of problems were superficially dissimilar from each other, whereas previous interleaved mathematics studies had required students to learn nearly identical kinds of problems. We conclude that interleaving improves mathematics learning not only by improving discrimination between different kinds of problems, but also by strengthening the association between each kind of problem and its corresponding strategy.

(Rohrer, D., Dedrick, D. F. & Burgess, K., 2014. “The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problems”. Psychon Bull Rev 21:1323–1330 DOI 10.3758/s13423-014-0588-3)

Step 3: Exercise 2 Constructing a Paragraph (~10-15 minutes)

Facilitator Notes:

The following is an exercise meant to get the students thinking about how a paragraph is organized to make an argument. It uses something easy to understand but still demands that there needs to be logical connections. The facilitator can point out to the students that the same principles of organization apply to the paragraphs they are about to read in the article in the next step.

Distribute Exercise Sheet 2 – Ordering Sentences into Paragraphs (PDF, 130 KB). Instruct students to read the sentences and then re-organize them into logical, linked paragraphs. They can just number the sentences rather than re-write them, although students may find it easier to see the logical connections if they write them out.

Step 4: Reading to Identify Parts of an Argument (~15 minutes)

Facilitator Notes:

This exercise is meant to be short. The facilitator should have already identified the paragraphs he or she has chosen to assign to students. Paragraphs in the first two sections or in the discussion section of the article may be most useful. The students are only to identify the parts of the paragraphs they are assigned. Most of the paragraphs in this article are relatively short, so should not take that long to read. Students need not understand every word in the paragraph to identify the claim, evidence, etc. The instructor can point out to the students that authors often use words like “The evidence suggests that…. Or “We claim that….”

Divide the group into pairs. Assign each pair one paragraph in the article to identify the claims, the evidence, any qualifiers, and the justification. Do not use more than 5 minutes for reading. After the pairs have finished, ask them to share their claims, evidence, justifications, etc. Call attention, in particular, to the use of words such as “because, as a result, even though, etc.” as well as order of sentences to show relationships between the ideas.

Step 5: CRAAP Test (~15 minutes)

Facilitator Notes:

This step is meant to introduce students to one commonly accepted method of evaluating sources used in an argument. Students are asked to choose one of the references from the article and do the CRAAP Test (PDF, 130 KB) on it. They are expected to Google authors, publishers, etc. in order to make their best judgments about the quality and appropriateness of the source they choose.

• Currency—is the article current? Currency is usually thought of as in the past five years, however, some seminal pieces of research or books written 15 or more years ago may still be current. Standards and regulations change more slowly, so these topics can have a longer period of currency. Something in fields like biomed or artificial intelligence etc., is probably measured in much shorter time periods.
• Relevance—is the content of the source relevant to the question or subject being considered?
• Authority—does the author (or authors) have authority in the subject? Although Steve Jobs may have been an amazing designer, he probably had little authority when it came to the best way to raise puppies.
• Accuracy—how accurate do you judge the information to be? Information supplied by most government sites is usually more accurate than information supplied by a marketing site. Information provided by a standards organization such as Underwriters Laboratory is usually more accurate than information provided by a blogger.
• Purpose—For what purpose was the information produced? If the article or information was produced to persuade readers or to convey information, the content may be different. If the purpose is aligned with the person using the information, it is probably more reliable or useful.

Step 6: Writing an Argumentative Paragraph (~20 minutes)

Facilitator Notes:

Students should have some idea of what interleaving vs blocked practice with mathematical problems is all about. (Note: Interleaving refers to switching from one subject or type of problem to another in a set time. Blocked practice refers to focusing on only one subject or type of problem for an extended period of time.) They are all familiar with “problem sets” and learning new strategies and formulae to use in solving problems.

Writing a paragraph that makes a claim about one way of learning new formulae, using evidence from the article or their own experience, should not be too challenging for the students. Students need only make one major claim.

Based on the work the students have done, ask each student to write one paragraph making an argument about the efficacy of interleaving or blocked study practices. At the end of 20 minutes (or earlier if most students have finished) each student gives his or her paragraph to a partner. The partners mark what they see as the claim, evidence, and justification.