Exploring the Use of Statistics Curricula with Annotated Lesson Notes

Figures & data

Fig. 1 The STEW lesson plan template with some prompts for annotated lesson notes highlighted.

Fig. 2 Examples of annotated lesson notes (written in blue italicized front) from a lesson plan on margin of error.

Table 1 The topics of each lesson plan and the corresponding content standards (NGA 2010).

Lesson	Topic and expected length	Common core content standard
Lesson 1	Observational Studies versus Experiments Two 50-min class periods	HSS.IC.B.3–Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Lesson 2	Interval Estimation and Margin of Error Two 50-min class periods	HSS.IC.B.4–Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Table 2 A categorization of types of annotated lesson notes.

Type of ALN	Description and example
Enhance Student Understanding	Ways a teacher may enhance their students’ statistical and conceptual understanding during instruction. $•$ Ex: Ask students, “How is one dot [in the sampling distribution] created?”
Recommendations & Reflections	Strategies, recommendations, and reflections provided by other teachers who have implemented a similar or previous version of the lesson plan. $•$ Ex: For this activity, we have found that groups of 2 with 1 computer work well.
Sample Student Responses	Sample student responses to teacher-led prompts and activity questions to help the instructor anticipate how students may respond to questions during instruction. $•$ Ex: Sample Student Responses: “The real average snowfall will be between 21 and 25 inches.”
Statistical Focal Points	Descriptions of the main statistical ideas present in the lesson and the activity problems that address them (if applicable). $•$ Ex: Problem $\#$12 is a very important question and addresses one of the main advantages of a randomized experiment.
Student Conceptions & Challenges	Descriptions of different ways students may conceive statistical ideas and identifications of common challenges students may encounter. $•$ Ex: Of these questions, $\#$3 may be the most challenging for students because they may focus on the sample rather than the entire population.
Supplemental Questions	Supplemental questions to help motivate content or extend the lesson plan. $•$ Ex: The following questions can replace Problem $\#$13 and provide students additional practice using the web applet to investigate categorical lurking variables within the context of randomized experiments.
Technology Use	Descriptions of when using technology may enhance instruction, along with instructions for using technology. $•$ Ex: A hidden feature of this web applet is the ability to click on a single dot in the plot. When you click on a dot, a table will appear, displaying the proportions for the treatment and control groups.

Table 3 Background information for each participant.

	Karen	Robin
Context of algebra class	Daily schedule: 50-min class periods each day with statistics content standards added near the end of the year	Block schedule: alternating days with 75-min class periods with statistics content standards integrated throughout the year
Classroom technology	Each student had access to a personal Chromebook	Each student had access to a personal iPad
Statistical preparation in college	Introductory statistics course	Introductory statistics course Graduate-level statistics course
Degree	BS Secondary Mathematics Education MS Undisclosed Field	BS Secondary Mathematics Education EdD Mathematics Education
Experience teaching statistics	9 years teaching AP Statistics	10 years teaching AP Statistics

Fig. 3 A summary of how teachers’ instructional actions compared (i.e., aligned, varied, and adapted) to annotated lesson notes (ALNs) which prescribed actions that could be observed during each lesson’s implementation.

Fig. 4 A dot plot Robin made from her class’s data.

Table 4 A classroom conversation that occurred in Robin’s class about the meaning of “one dot” in a sampling distribution.

Robin:	We need to be very clear about this [pointing to one dot in Figure 4]. So, who can tell me—what does this one dot mean?
Student:	If you did one test. That’s …
Robin:	If I did one resampling, then …
Student:	The percentage of people that listen to music would be that [motioning to the value of one dot displayed in Figure 4].