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The TQE Process in Small-Group Instruction

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Consider how changing the constraints of the task could provide students with more opportunities to engage in sense making. A well-constructed task allows the teacher to determine whether students lack necessary understanding of the learning goal. Consider the following cookie-sharing task, also involving four cookies being shared among five friends (figure 2.4). Brandon shared four cookies equally among himself and his four friends. He started by giving each person half of a cookie as illustrated here (the letters stand for which person will get that piece):

A

B

C

D

E

Now continue sharing the cookies for Brandon until all four cookies have been shared. How much of a cookie will each person receive?

Source: Dixon, Nolan, Adams, Tobias, & Barmoha, 2016, p. 73. Figure 2.4: Cookie-sharing task.

Note how the task increases the cognitive demand required of students by preventing them from simply dividing each cookie into five pieces. What type of thinking would students have to engage in to solve this task? Figure 2.5 provides an example of what a student might draw to solve the task.

A

B

C

D

A

C

B

D

E

E A

Source: Dixon, Nolan, Adams, Tobias, & Barmoha, 2016, p. 73. Figure 2.5: Cookie-sharing task solution.

After drawing out the portions as illustrated in figure 2.5, the next step would be to name the pieces of cookie that Person A would receive. It is clear that Person A would receive ½ of the first cookie. The other cookie parts are often more challenging for students to name. What common errors might be elicited from students as they work to name the other cookie pieces? What common error would a student be making if the student named the next largest piece Person A would receive as ⅓? What about if the student named the smallest piece Person A would receive as 1/5? These common errors are intentionally inherent in the task. It may be new to you to consider a problem worthwhile because it has the potential to elicit common errors. However, it makes sense when you consider that you would prefer to address those errors during small-group instruction, rather than to see them on a summative assessment.

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Making Sense of Mathematics for Teaching the Small Group  

Make sense of effective characteristics of K–5 small-group instruction in mathematics. Connect new understandings to classroom practice thro...

Making Sense of Mathematics for Teaching the Small Group  

Make sense of effective characteristics of K–5 small-group instruction in mathematics. Connect new understandings to classroom practice thro...