Statistics involves the construction, collection, classification, analysis, and interpretation of numerical data. Using statistics involves more than determining frequencies or calculating the mean. It includes constructing, reading, and interpreting data and using statistics as evidence in arguments. Individuals need understandings of statistics to analyze real-world situations, make conclusions based on data, and appreciate the contributions statistical thinking can make in our decision-making.
Unfortunately, many students do not have the strong conceptual understandings of data needed to be able to reason statistically. As students gain experience with conducting investigations and analyzing data, they will confront and hopefully resolve these difficulties. Furthermore, students often have a negative affect towards or opinion about statistics. This affect, combined with an insufficient ability to think critically about data and weak foundational understandings of basic statistical concepts, prevents students from pursuing higher levels of STEM education and careers. Students need instruction in statistics to meet the Common Core State Standards in Mathematics that relate to statistical reasoning. Beyond the classroom, it is imperative to develop students’ statistical understandings at a young age to prepare them for understanding and using statistics in their daily lives and to inspire them for future educational and career opportunities.
The Diagnostic Statistics Assessment (DSA) project addresses these needs with resources to assess and develop students’ understandings, knowledge, and affect related to statistics. The DSA materials are intended to help middle school teachers supplement their regular curriculum materials to immerse their students in and maximize students' learning of quantitative literacy skills. The DSA resources include teacher tutorials about key concepts and misconceptions in statistical investigations, diagnostic assessments to identify students reasoning with misconceptions related to statistical investigations, and student activities to support development of understanding related to statistical investigations.
This page provides an overview of all of the resources available through the DSA. The picture below is the recommended sequencing of how to best use the resources.
The teacher tutorials cover key ideas related to statistical investigations and are intended to provide teachers with a deeper understanding of the teaching and learning of statistics. Before using the classroom activities with students, teachers should review the tutorials and consider the reflection questions at the end of each tutorial. During the process of using the classroom activities, teachers may benefit from revisiting the relevant tutorials and reviewing them with the added perspective of seeing what students do during classroom lessons. Below, is a brief introduction to the four steps of a statistical investigation .
Steps of Statistical Investigations Tutorials
Each tutorial focuses on one step of statistical investigations and explains how to support students in that step. While the process of a statistical investigation may be iterative, we focus each tutorial on one step at a time in order to provide details and an appropriate level of student support. Throughout the tutorials, we have threaded data stories and vignettes about what might happen in real classroom lessons on statistical investigation. These data stories seek to illustrate the steps of a statistical investigation in context and provide examples of how students might interact with that particular step. One data story is set in Andrea’s 7th grade class where students are investigating statistical questions based on an existing data set about the International Space Station. Another data story is set in Richard’s 6th grade class where students are investigating questions about the impact of a Healthy Habits educational program focused on sleep, exercise, and nutrition.
Step 1: Formulate Questions. To begin the process of a statistical investigation, the typical first step is formulating a statistical question. Statistical questions motivate the analysis of data and ground the statistical investigation. Understanding, explaining, and quantifying variability in data are essential to statistics, and this process starts with a statistical question that focuses on data that vary and can be answered through a statistical study rather than getting an exact answer from a book, individual, or website..
Step 2: Collect Data. To address a statistical question, individuals can use existing data or collect their own data. When collecting data, the investigator needs to consider what to measure and how to measure it in light of their question. They need to consider different types of data, how the variables of interest influence the selection of data, and possible data collection methods and tools. It is important to consider all elements of data collection, even when using existing data.
Step 3: Analyze Data. In middle school, the goal is to use descriptive statistics and graphs to describe the central tendency and variability that exists in the data’s distribution. Data analysis includes representing the data graphically, selecting appropriate graphs, summarizing graphically displayed data, and selecting appropriate summarizing characteristics.
Step 4: Interpret Results. During the process of a statistical investigation, individuals move from analysis of data to interpretation of results. The goal of interpreting results is to make sense of the variability that exist in the data and relate the collected data and analysis back to the statistical question.
Misconceptions often represent knowledge that is underdeveloped or knowledge that is productive in some contexts, but has been over-generalized. The DSA focuses on three misconceptions: Data Distributions as Entities (DDE), Comparing Data Distributions (CDD), and Overreliance on the Mean Procedure (OMP). For each of these misconceptions, there is a tutorial describing the misconception, the student behaviors indicative of that misconception, information about why students may struggling, and suggestions for how teachers can facilitate student understanding. Teachers should read these tutorials prior to administering the assessments so they have a good understanding of the targeted misconceptions.
Data Distributions as Entities: Many students enter middle school with an incomplete understanding of data. They consider the fundamental unit of a data distribution related to be either the individual cases or groupings of cases with similar values; they fail to develop a statistical conception of a data distribution as an entirety with characteristics that are different from the characteristics of the individual data values that make it up. Students with the DDE misconception do not perceive a data distribution as a single, unified entity with its own characteristics, unique from those of its individual data points.
Comparing Data Distributions: Many middle grades students find it difficult to compare data distributions based on their summary measures. It is important for students to be able to compare data distributions based on summary measures so their comparisons are based on accurate characterizations of the data and so they can draw comparative inferences between two distributions. Rather than compare distributions of values based on appropriate representative values or summary measures, students with the CDD misconception compare distributions using individual data points in each distribution (such as minimums or maximums); particular groups or clusters of data like slices, segments, or cutoff points; totals, values, or points calculated from data distributions with different sample sizes; or ranges from distributions that vary in shape
Overreliance on the Mean Procedure: Students reasoning with the OMP misconception can follow the procedure to compute the mean by adding all of the values and dividing by the number of values added but do not present statistical understanding of the mean and/or do not present mathematical understanding of the mean. When using the mean procedure without statistical understanding, students may not be coordinating their understanding of the mean procedure with what the mean can say as a measure of central tendency, and they may struggle to connect calculated means to graphic displays of the data or the context. Students reasoning without mathematical understandings of the mean may struggle to understand their calculations, relations between data and their calculated means, and how the mean relates to the range and any changes in data values.
Teachers can use the diagnostic assessments to identify students who are consistently reasoning with one of the three targeted misconceptions. The materials include a pre- and post-test assessment for each misconception.
Each pre-test includes multiple-choice and technology-enhanced items targeting one of the three statistical misconceptions. All items are computer-scored and teachers receive instant feedback reports about their students’ performance. The reports identify students who may be reasoning with particular misconceptions. Teachers can use this information to tailor instruction for these students using DSA supplemental activities (described below). Teachers can then use the post-test to measure changes in students’ understanding.
It is important to note that the assessments used to diagnose whether students are reasoning with the DDE and CDD misconception use dot plots and bar graphs. Your students should be at least generally familiar with these kinds of data presentations. If your students have never seen one of these data displays, it is not appropriate to use the assessment to diagnose DDE or CDD reasoning. Similarly, the OMP misconception describes students who know the procedure for calculating the mean. If your students do not know the term "mean" or do not know the procedure for calculating the mean, it is not appropriate to use the assessment to determine whether students are reasoning with the OMP misconception.
The DSA includes seven whole-class student activities. Each activity is designed to improve statistical understandings and affect for all students, regardless of whether they show evidence of misconception reasoning. The DSA also includes nine supplemental activities designed specifically for students identified as reasoning with the targeted misconceptions. These activities are designed to support the process of helping students reshape their statistical ideas.
All teachers are expected to use the Foundational Activity, but teachers do not need to use all of the other activities. Each teacher should select the activities that most closely match the needs of his/her particular students. The guide below is designed to help teachers make the optional match between the DSA activities and their students.
Classroom Activities: There are seven activities for the whole class: Foundational Activity, Measure of Center Activity, Measure of Spread Activity, Statistical Questions Activity, Data Collection Activity, Data Analysis Activity, and Interpretation Activity. The activities are designed for 6th and 7th grade students reasoning at Level A (beginning awareness) and Level B (increased awareness) . The activities use a variety of problem contexts and are designed to be engaging to middle school students. Most activities use existing datasets, but some activities involve data collection to allow students the opportunity to experience this aspect of statistical investigation. The activities range from 1 to 5 class lessons and include a Teacher Guide, Student Handouts, and PowerPoint slides.
The Foundational Activity is the only activity intended for use by all teachers. This activity serves as an introduction to all four steps of statistical investigation and emphasizes all steps equally.
After completing the Foundational Activity, if students need additional background or support in measures of center and/or spread, teachers should use the Measures of Center Activity and/or the Measures of Spread Activity.
Teachers can also engage students in a second activity focused on a single step in the statistical investigation process. Teachers should consider the step(s) that students would most benefit from focusing on: Statistical Questions Activity, Data Collection Activity, Data Analysis Activity, or Interpretation Activity.
Supplemental Activities: There are three Supplemental Activities provided for each misconception. These activities are designed specifically for students identified by the diagnostic assessments as reasoning with a targeted misconception. In order to support students’ developing statistical reasoning, the supplemental activities are based on research about how students can challenge and reconstruct their understandings related to a topic, thereby addressing misconceptions and refining their knowledge for specific contexts. The Supplemental Activities are single-lesson activities designed to complement the Classroom Activities (e.g., using similar data contexts) and can be used with individual students or small groups.
Practice Tasks: There are a small set of practice tasks included for each misconception. Teachers can use these as an informal guide to whether initial Supplemental Activities have been successful at helping students that were identified as reasoning with the misconception reorganize their thinking. These tasks can help teachers decide if those students need additional work with more Supplemental Activities.
Begin with the Teacher Tutorials!
Note that you can always return to this introductory page by clicking on the DSA logo at the top-left of the screen and the clicking Start here!