Evaluate This! Drawing Conclusions with Statistics
Institute for the Study of Knowledge Management in Education
UNIT TEMPLATE: Text-Based STEM Inquiry
This template provides an approach for creating a science investigation that includes reading-focused inquiry to build student science literacy skills. The template was created to support library media specialists and STEM teacher cohorts in the School Librarians Advancing STEM Learning project, led by the Institute for the Study of Knowledge Management (ISKME) in partnership with Granite State University, New Hampshire, and funded by the Institute for Museum and Library Services (IMLS).
Part I: Unit Title: Evaluate This! Drawing Conclusions with Statistics
Part II: Background on LMS and Science Teacher relationship : This lesson was created by Library Media Specialist Kim Carter and mathematics teachers Alaura Carson and Jen Spoerke. Jen’s strengths include selecting standards and subjects that are suitable for literacy lessons particularly with integrating writing in math. Alaura’s strengths are mathematical content knowledge and a willingness to collaborate. Kim’s strengths are inquiry-based instructional design, curation of resources, and knowledge of open-source materials.
Jen is interested in learning more about OER, how to share and organize resources for others’ uses, and how to integrating reading in math. Alaura is interested in learning how to incorporate literacy in a mathematics class. Kim is interested in learning more about the statistics content and skills and how Alaura and Jen scaffold students’ conceptual understanding and practical applications.
Part III: Unit Description: This unit includes 10 unit days and our blocks are 90-minutes long. Through the interpretation of making inferences and justifying conclusions based on statistical data, students will come to a better understanding of mathematical evidence and reason. Our lessons will culminate in students presenting their findings comparing local to national data regarding the relationships between educational attainment and financial earnings. Students will have options for different presentation media (web-based, face to face, pamphlet, etc.) and audiences (peers, parents, community members). Over the course of the unit, students will explore a variety of texts and grow in their knowledge of data collection and evaluation to write their own report.
Part IV: Standards
CCSS Mathematics Standards
- Make inferences and justify conclusions while evaluating reports based on data.
- Make inferences and justify conclusions from sample surveys, experiments, and observational studies (http://www.corestandards.org/Math/Content/HSS/IC/)
CCSS.MATH.CONTENT: HSS.IC.B.6 : Evaluate reports based on data.
CCSS Mathematical Practices
- Reason abstractly and quantitatively.
- Look for and make use of structure.
CCSS Science Literacy Standards
- CCSS.ELA-LITERACY.RST.9-10.7: Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
Part V: Unit Essential Question: What inferences and/or conclusions can be drawn from relationships between data sets?
Part VI: Goals for Using Inquiry: The goal for using inquiry in this unit is to have students make inferences and draw conclusions based on data and select their own additional resources to develop an answer to the unit’s essential question. The math teachers and the media library specialist have selected an anchor text presenting statistical data on educational attainment and annual earnings of young adults. Supporting texts provide resources for students to further consider when making personal meaning of statistical data.
The goal for using inquiry in this unit is to have students examine the anchor text as an open invitation to inquiry about drawing conclusions from statistical data. Using the anchor text “Annual Earnings of Young Adults” (NCES, 2016) as the base and 2 supportive texts, including “3 Ways to Spot a Bad Statistic” and Community Profiles for each campus’s city (Keene and Manchester), students will develop their own set of inquiry questions (ex: “I wonder…”) for a comparing local data to the national data presented in the anchor text. Students will narrow down their inquiry questions to one specific, targeted question that they seek to answer through the culminating activity.
Part VII: Summative Assessment Description and Rubric
Summative Assessment - Students will find local data similar to the supporting text and draw conclusions from the data. Students will make inferences about why the data is or could be different by creating a report that highlights key data to support their conclusions.
Rubric -
| Category | Exemplary (7) | Proficient (5) | Progressing (3) | Emerging (1) |
| Research/Statistical Data | Students include 4 or more examples or pieces of data to support their claim from a reliable source. | Students include at least 3 examples or pieces of data to support their claim from a reliable source. | Students include at least 2 examples or pieces of data to support their claim from a reliable source. | Students include fewer than 2 examples or pieces of data to support their claim from a reliable source OR the examples or pieces of data to support their claim are from an unreliable source. |
| Sources - Citation | Information in all source citations is correct and in the format assigned. | Information in all source citations is correct but there are minor errors in formatting. | Information in almost all source citations is correct AND there are minor errors in formatting. | Information in some source citations is correct OR there are major errors in formatting. |
| Product | Students create an original, accurate and interesting product that makes a compelling case. | Students create an accurate product that makes a compelling case. | Students create an accurate product but it does not make a compelling case. | The product is not accurate. |
| Writing - Organization | Each section in the final product has a clear beginning, middle, and end. | Almost all sections of the final product have a clear beginning, middle and end. | Most sections of the final product have a clear beginning, middle and end. | Less than half of the sections of the final product have a clear beginning, middle and end. |
| Type of Graph Chosen | Graphs fits the data well and makes it easy to interpret. | Graphs are adequate and do not distort the data, but the interpretation of the data is somewhat difficult. | Graphs distort the data somewhat and the interpretation of the data is somewhat difficult. | Graphs are included but seriously distorts the data making interpretation almost impossible. |
| Relates Graphics to Text | Student accurately explains how each graphic/diagram is related to the text, and accurately determines whether each graphic/diagram agrees with the information in the text. | Student accurately explains how each graphic/diagram is related to the text. | Student accurately explains how almost all of the diagrams are related to the text. | Student accurately explains how some of the diagrams are related to the text. OR student has difficulty relating graphics and diagrams to the text. |
Part VIII: Prior Knowledge Needed
Summarize, represent, and interpret data on a single count variable and double count variables; interpret linear models
- Interpret and graph data on/with bar graphs, histograms, box-and-whisker plots, pie charts, scatter plots, and line graphs
- Describe how two variables are related to each other (correlation and/or causation)
- Use regression models to fit a function to data
- Understand slope as being synonymous with rate of change and the intercept as being the constant term
Part IX: Student Learning Objectives
- Students will be able to analyze a report based on data by translating information expressed through graphs into words.
- Students will be able to analyze a report based on data by translating quantitative or technical information expressed in words in a text into visual form.
- Students will be able to formulate hypotheses by analyzing and interpreting data.
- Students will be able to formulate and justify a conclusion by analyzing and interpreting data.
Part X: Text Set Description (used to analyze the purpose and goal of each text they provide to the students)
Text Title & Hyperlink
Text Purpose
(discuss complexity of the text along with its purpose/goal )
Text-Dependent Questions (created by the teacher/librarian to help students analyze the text in a specific sequence)
Accommodations for Diverse Learners
| “Annual Earnings of Young Adults” Anchor Texthttps://nces.ed.gov/programs/coe/indicator_cba.asp(pdf link: https://nces.ed.gov/programs/coe/pdf/coe_cba.pdf) | This is our Anchor Text, designed to provide data and graphs about the financial earnings of young adults in relation to educational attainment while provoking student engagement around the essential question.The ATOS level of the text is 10.7, which is appropriate for slightly above the middle of a 9th grade year. Linked here is the Qualitative Analysis of the Complexity. | 1. What question did the author seek to answer?2. What variables are represented by the data in this article? 3. Is the data categorical or quantitative? 4. Which data was most meaningful to you? Why?5. Why did the authors choose median rather than mode or mean? 6. What inferences can you make from the data?7. What further questions does this article raise for you?8. Based on the data in this article, what hypotheses would you like to test with further data?9.Would you represent the data using the same graphs the author did? Why or why not? | 1. Glossary definitions from the NCES report will be made available and reviewed before reading the article.2. The first graph and text will be read and analyzed as a whole group, modeling the process. The remaining three will be read and analyzed in small groups, with support as needed. |
| Supporting Text #1 | Mona Chalabi: 3 ways to spot a bad statisticMona Chalabi TED talkAnd Transcript | 1. Did you have different reactions to the different representations of data?2. Has your answer to question 9 (with anchor text) changed? If so, how? If not, why not? | 1. Make the link to the video available to students to review/rewatch as needed2. Make transcript available to students so that they can read along and make annotations as needed |
| Supporting Text#2https://www.nhes.nh.gov/elmi/products/cp/profiles-htm/manchester.htmhttps://www.nhes.nh.gov/elmi/products/cp/profiles-htm/keene.htm | {Optional qualitative and quantitative analysis}These texts present community level data related to employment and education attainment. (The data sets do not correlate the two variables.) | 1. Does this data correlate with the information in the anchor text?2. Which data table is most effective at communicating the data collected by the researchers?3. What information is needed to be able to compare local data to national data?4.What’s your hypothesis about the local relationship between educational attainment and annual earnings? | 1. Clearly identify the data that will be focused on by highlighting or circling the data |
Part XI: Suggested Lesson Breakdown/Pacing
Day
Student Learning Objectives
Aligned Student Learning Task and Suggested Timing
Formative Assessment
Important Accommodations
| One (90 minute block)(Manchester Campus 5/5 and Keene Campus 5/8) | Anchor Text dayStudents will be able to formulate hypotheses by analyzing and interpreting data. | Pre-Class Survey.1. Open with survey results and discussion. How do your (anonymous) answers compare to others’? What do you think is a reasonable amount to earn in one year?2. Class collaboratively defines vocabulary terms and reviews related terms from the report Glossary.3. Kim (LMS) leads 3 rounds of close-reading to answer questions 1-5 (close reading 1: question 1; close reading 2: questions 2,3; close reading 3: questions 4, 5) (Handout is here.)4. Students will discuss the article to address questions 6-85. Use question 9 as opening to Supporting Text #16. View the video for Supporting Text #17. Alaura or Jen will lead a discussion on how or if students responses to question have changed8. Students will write a reflection about what they learned from the close readings and discussions. | 1. The (teacher/LMS) will monitor students as they read independently to observe the number of annotations made.2. The (teacher/LMS) will monitor student recording of teacher recommended annotations.3. The (teacher/LMS) will monitor paired discussions of the anchor texts questions.4. The (teacher/LMS) will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | 1. Vocabulary will be discussed together prior to the reading.2. The first section will be read and discussed together.3. Students will discuss anchor text questions in pairs while the teacher and LMS circulate, monitoring understanding and discussion, providing prompts and support as needed. |
| Two (90-min block)5/8 & 5/10 | Students will come to a better understanding of graphical representation | 1. Review of day 12. Discussion of questions for supporting text #1.3. Have students choose at least 1 graph from the anchor text and represent it in a different form.4. Revisit questions 7 & 8 from the anchor text and begin preliminary research.5. Students will write a reflection about what they learned by creating a new graphic representation and conducting their research. | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | 1. Students will have access to tech to create their graphical representation (as needed) |
| Three (90-min block)5/10 & 5/12 | Lesson went well, but may not be directly related to the unit goal.Students will be able to analyze a report based on data by translating information expressed through graphs into words.Students will be able to analyze a report based on data by translating quantitative or technical information expressed in words in a text into visual form. | 1. Notes and discussion on hypothesis testing and comparing two data sets using a box-and-whisker plot to see if there is a difference in the data.2. Complete practice problems on hypothesis testing3. Revisit questions 7 & 8 from the anchor text and continue research.4. Students will write a reflection about what they learned by completing the practice problems on hypothesis testing and conducting their research.1. Have students reread/review the anchor text2. Choose a chart and write a one paragraph description of the data represented in the cart3. Choose data not represented graphically and create a graphical representation of the data4. Students will write a reflection of pros vs. cons of data represented by words and graphical representations | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | 1. Students will have access to tech to create their graphical representation (as needed)2. Students will have paragraphs read to them to aid in creating graphical representation (as needed)3. Students will be assessed on concepts rather than grammar and spelling for the paragraph description4. Students may work in pairs (or small groups) to permit discussion and out-loud-thinking |
| Four (90-min block) 5/15 & 5/17 | This lesson didn’t work at all, says Alaura. Let’s just cut it from the unit plan. Jen agrees.Students will be able to formulate hypotheses by analyzing and interpreting data. | 1. Look at supporting text #2 and answer accompanying questions via a think, pair, share activity2. Research for 45 minutes the hypothesis you (or your team) came up with so that it can be either rejected or accepted3. “Present” your findings to the class Discuss as a class what makes data comparable to other data4. Begin to define the project Create a list of “I wonder…” questions based on the data in the text5. Students will write a reflection about the direction they want their personal project to go in based on the research they’ve done so far. | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed.2. The teacher will help guide the discussion to avoid tangential conversations | 1. The teacher and students will preserve quiet time to allow for various processing speeds |
| Five (90-min block) | Students will be able evaluate reports based on data. | 1. Rewatch the video (with transcript available for highlighting key points) to find the three ways to spot the bad stats2. Evaluate the anchor text with the three questions3. Evaluate the secondary text with the three questions4. Do a comparison between the two texts to see which one is the better statistical report of the two | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the comparisons before the next class period to determine if any review is needed. | 1. Students will have the transcript2. Check in after the video to determine whether or not the students “found” the three questions |
| Six (90-min block) | Students will be able evaluate reports based on data.Students will be able to formulate hypotheses by analyzing and interpreting data. | 1. Debrief the comparison of the two texts2. Identify what the student’s wish to investigate (earnings vs. education, earnings vs. gender, etc.)3. Create questions to gather data via a google survey (shared via school communications and social media) | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed.2. Encourage students to use their list of “I wonder” from day Four to create their investigation. | 1. The teacher and students will preserve quiet time to allow for various processing speeds |
| Seven (90-min block) | Students will be able to formulate a conclusion by analyzing and interpreting data. | 1. Review and analyze the data collected2. Prepare reports of data, data analysis, and conclusions. | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | |
| Eight (90-min block) | Students will be able to formulate a conclusion by analyzing and interpreting data. | 1. Complete preparation for presentation of reports2. Receive feedback from peers on reports using the rubric | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | |
| Nine (90-min block) | Students will be able to justify a conclusion by analyzing and interpreting data. | 1. Presentation of reports to outside panelist(s) | 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | |
| Ten (90-min block) | Students will be able to justify a conclusion by analyzing and interpreting data. | 1. Debrief the unit with students (discussion)
| 1. The teacher will monitor progress to see if certain areas of the assignment are confusing. The teacher will read the reflections before the next class period to determine if any review is needed. | 1.The teacher and students will preserve quiet time to allow for various processing speeds |
Part XII: Attachment of Student Work Examples
(Please include links or attachments of 3 work samples that have been scored using your rubric and have feedback from both STEM teachers and the LMS. Consider including both exemplars and samples that have room for improvement. Please do not include student names or pictures.)
Google folder with student work from Jen's class
Google folder with student work from Alaura's class
Part XIII: Teacher and Librarian Reflection on the Implementation of the Unit
Kim Carter - Librarian: There were plenty of surprises for me in the implementation of our Unit, from our initial implementation to how students engaged with the unit context and tasks to the resulting outcomes.
Initial implementation: In retrospect my first surprise - my team members’ discomfort with teaching reading literacy strategies - shouldn’t have been a surprise at all and is likely more a measure of an unfortunate loss of perspective on my part as my role has decreased my direct connection with daily instructional practice. I honestly don’t know any math teachers who have been taught or have been expected to develop reading literacy instructional skills. Therein lies some of the obvious value of the collaboration! Unfortunately, my availability for co-teaching and collaboration beyond the planning process and the anchor text lesson was limited and I feel was not as effective a team member as I needed to be.
My availability also impacted my interactions with the students. Even though they all knew me, they were definitely not used to having me in their math class. One takeaway is that to be a full collaborator through implementation of the unit, the librarian partner should be involved throughout the unit, not just during the anchor text lesson.
Student Engagement : Generally speaking, students are both MC2 campuses attend MC2 because they want an alternative to traditional classes. Classes are called learning studios with the idea that they’ll be project- and problem-based, a concept that can be a bit more challenging for math curriculum. Add to that the fact that all MC2 learning studios are heterogeneous, across ages and abilities. While students select the learning studios they want, they also have to pay attention to credits they need. All of the above is to say, students in MC2 learning studios are pretty immediate in communicating (verbally or nonverbally) whether or not learning activities are engaging them.
Observations from the anchor text lesson include:
- Many students were startled that they were being expected to read an article.
- The focus topic we selected - the relationship between educational attainment and financial earnings - missed the mark. Students at each campus were more intrigued by the gender differences in earnings than the relationships to educational attainment (a couple pursued this question in their personal projects.)
- Virtually all students were highly engaged by Supporting Text #1 - 3 Ways to Spot a Bad Statistic. Starting with this engaging video/transcript combination may more successfully hook students into the subsequent anchor text work It would also be worth considering using the combination of the video with its transcript as the anchor text itself.
Resulting Outcomes : While many students completed the tasks for the unit, fewer students completed the final projects. The students who did complete the work and wrote their final reflections noted skepticism of the value of the use of the anchor text and the explicit close reading activities. One student commented: “While I get the two [subjects] are connected, that is no excuse for sliding from subject to subject.”
Overall, I think we need to do a better job integrating and scaffolding literacy activities within our math instruction. Using high-interest topics to establish purpose and meaning for the use of the texts is particularly important with our often less than confident learners.
Jen Spoerke - Math Teacher
This unit was a challenge to incorporate into the class that we were teaching. I thought it was going to slide in with minimal disruption, but we moved slower through unit 1 then we were expecting to, so unit 2 (this unit) didn’t get as much build up as we were hoping which resulted in a rough introduction.
As a math teacher, I have never been taught how to teach literacy skills. I expect that kids come into my class with basic literacy skills that I can help them hone in the context of mathematics. I was very glad to have Kim come in to teach the literacy lesson because I would have botched if left to my own devices.
The kids struggled with the fact that they were expected to read and analyze a text. They also struggled with the notion of going back to the text again and again. It is a trend that I’ve noticed within academia (and I am guilty of it myself) that students are not thrilled with the idea of mingling different subject areas together. This was very apparent in this particular statistics class; many of the students lost interest in the class and few completed the final project.
I think it would have been helpful to have Kim involved for a longer period of time. When the kids began writing their report, it would have been great to have her there to tap into her literacy skills. I can let someone know that what they’ve written sounds weird, but not why or how to fix it.
If this unit is used again in the future, I think there needs to be a more solid connection to the previous unit and better differentiation for various literacy skills.
Alaura Bailey (Carson) - Mathematics Teacher
Planning this unit made me realize how much I miss being able to collaborate with other mathematics teachers and bounce ideas off of them when planning a unit. It was great to be able to work with Jen and share in the joy and struggles of planning the unit leading up to Evaluate This. We were able to share what went well with each other and change lessons as needed when one did not go as expected. It was great being able to work with Kim as well and having the library media specialist as another sounding board. However, it was difficult to collaborate cross campus with about 60 miles between us.
Having a template to follow was great. However, at points is was difficult to work with. I found it to be beneficial and a challenge to select the anchor text before beginning to plan the unit. We really had to think about the big picture of the unit when picking the anchor text. I also found the time constraints when of when the SLASL unit had to be taught a challenge. It made me feel as if some of the lessons leading up to the SLASL unit were rushed and not covered as well as I would have liked.
It was interesting watching the students learn from mistakes that they made when creating the survey. They wanted to leave many of the questions such as level of educational attainment as short responses rather than multiple choice. This lead them to have to interpret what some of the responses (such as 13 years of schooling or OJT) meant in terms of educational attainment.
I am glad that I had the experience of helping to create a text based unit and do see the value in doing so again in the future. One of the most eye opening realizations for me was that there were even literacy standards for technical subjects. Now that I am aware of them, I will be more conscientious of them when planning future units.
Licensed by ISKME CC-BY 2016