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Critical Thinking Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together. Creative thinking originates ideas that are assessed using Critical Thinking. Explore these strategies to intentionally support Critical Thinking as a Habit of Mind in your classroom. Infographic It! Want to develop critical and creative thinking skills at the same time? Ask students to evaluate and organize their data in a visual way. They must think critically as they evaluate the validity of their data and decide how to organize it. They must think creatively as they communicate their data in the form of a graph, drawing, or infographic. The more students exercise critical and creative thinking, the better problem-solvers they will be! Critical Thinking Sentence Stems Use these sentence stems to promote critical thinking: •Why did… •How do you know that... •Are you sure that… •What's your evidence that… Show Your Thinking Instead of saying, "Show your work," try saying, "Show your thinking." This emphasizes that you value critical thinking over rote memorization; working smart more than working hard. Where's the Evidence? Make a habit of asking, "Where's the evidence?" or "What's your evidence?" The more students hear you ask this question, the more apt they will be to provide evidence-based responses. By asking this question in multiple contexts, you encourage students to be lifelong critical thinkers. (For example, if a student says, "My mom is making meatloaf tonight," ask, "What's your evidence?") Five Whys When students answer a question or give an initial response, follow with, "Why?" They should give a slightly deeper answer and/or understanding. Follow that response with, "Why?" again. Continue asking "Why?" five times so students become accustomed to deeper and deeper levels of understanding.
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Critical Thinking - VAEI · Critical Thinking Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together.

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Page 1: Critical Thinking - VAEI · Critical Thinking Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together.

Critical Thinking

Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together. Creative thinking originates ideas that are assessed using Critical Thinking. Explore these strategies to intentionally support Critical Thinking as a Habit of Mind in your classroom. Infographic It! Want to develop critical and creative thinking skills at the same time? Ask students to evaluate and organize their data in a visual way. They must think critically as they evaluate the validity of their data and decide how to organize it. They must think creatively as they communicate their data in the form of a graph, drawing, or infographic. The more students exercise critical and creative thinking, the better problem-solvers they will be! Critical Thinking Sentence Stems Use these sentence stems to promote critical thinking: •Why did… •How do you know that... •Are you sure that… •What's your evidence that… Show Your Thinking Instead of saying, "Show your work," try saying, "Show your thinking." This emphasizes that you value critical thinking over rote memorization; working smart more than working hard. Where's the Evidence? Make a habit of asking, "Where's the evidence?" or "What's your evidence?" The more students hear you ask this question, the more apt they will be to provide evidence-based responses. By asking this question in multiple contexts, you encourage students to be lifelong critical thinkers. (For example, if a student says, "My mom is making meatloaf tonight," ask, "What's your evidence?") Five Whys When students answer a question or give an initial response, follow with, "Why?" They should give a slightly deeper answer and/or understanding. Follow that response with, "Why?" again. Continue asking "Why?" five times so students become accustomed to deeper and deeper levels of understanding.

Page 2: Critical Thinking - VAEI · Critical Thinking Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together.

Critical Thinking

FQR Format When asking students questions, have them respond in a FQR format. Have them answer the question with a Fact, then ask a related Question, then Respond to the question. For example, if you ask "Why did the bulb light?," students may answer as follows. Fact: Because the wires formed a complete circuit. Question: How fast does the current move through the wires? Response: I'll add that question to my journal to research later. The FQR promotes critical and creative thinking instead of basic recall. Worksheets Gone Wild When you have to use a worksheet, bolster its utility by using it as a tool to strengthen creative thinking skills. Have the students weave a story out of the answers on the worksheet. Have them connect something on the worksheet to something they have learned in another subject. Have them turn the worksheet into an infographic. Data Your Way Help students take ownership of their learning by allowing them to choose how they represent their data from an investigation. They may stretch in their abilities and learn a new way to graph or chart data. They may observe other students’ representations and want to learn that method. Or you may want to share a variety of graph choices to spur their thinking, such as those presented in this Graph Choice Chart. When students take ownership of their learning, engagement increases. A Dot for your Thoughts Draw a dot on the board. Have students brainstorm a list of what the dot could possibly represent (basketball, eye, star, etc.). Then ask the group to create categories out of the ideas listed so far (sports, art, space, etc.). Resume the brainstorming, this time filling up the newly created categories. Going between divergent thinking (creative brainstorming) and convergent thinking (critical categorization) can yield more varied ideas and better focus. As students brainstorm, allow for new categories and also discuss any unique ideas that couldn't fit in a category. Mystery Box Pick an object, for example, a banana. Observe it carefully. Place the object in the box. Have students take turns asking yes/no questions about the object. When they think they know what the object is they should ask a question to prove it. When a large number of your class believes they know the answer, count to three and have them speak the answer out loud. You can pick students to take your place as the leader.

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Critical Thinking

Compare and Contrast Having students explain similarities and differences they find between two processes or concepts is a great way to promote critical thinking. Use a Venn diagram or other graphic organizer to represent similarities/differences visually. Students could compare needs of plants and animals, land formations in different states, math problems that have the same answer, etc. Turn Data into Evidence Having students transform data into evidence is a powerful strategy to promote critical thinking. Guide students in first evaluating their data for trustworthiness, then analyzing the data for patterns and trends. This could include organizing and representing the data visually. Finally, have them interpret the data in a way that conveys meaning and understanding. Idea Snowball Utilize a variety of collaborative structures to develop and refine ideas. Use individual think time to reflect on a reading, video, or topic. Use small group time for students to share their thoughts with others and develop their ideas, and use whole group time for discussion that allows for refinement of learning. Like a snowball rolling down a hill, each structure adds layers of insight to the original idea. Think-Aloud Model self-direction and metacognition by thinking aloud. You can share your rationale as you design an investigation plan so that students learn to emulate that thought process when they design their own investigation plans. You can share possible reasons for a particular result so students see what ongoing critical thinking looks like. Thinking aloud also supports a culture of risk-taking by modeling the communication of ideas freely and without judgement. Fact-Question-Connection Format When curious people learn new information, they continue to ask questions and make connections. Develop curiosity by encouraging students to share their learning from secondary resources using a Fact-Question-Connection format. They should share one fact they learned, one question they still have, and one connection from what they learned to something they already know, something they are interested in, or something another classmate said.

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Data literacy is complex. When students investigate the natural world, they must be able to gather data, organize it in tables and spreadsheets, analyze it

in context, and describe and interpret it—usually as evi-dence to support a scientific argument (Jiménez-Aleixan-dre, Bugallo Rodríguez, and Duschl 2000; Kilpatrick 1985; Schoenfeld 1992).

These skills are echoed in the science and engineering prac-tices of the Next Generation Science Standards: “Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evi-dence” (NGSS Lead States 2013, Appendix F, page 9).

Hannah Webber, Sarah J. Nelson, Ryan Weatherbee, Bill Zoellick, and Molly Schauffler

But before students can identify patterns in data or use it as evidence, they must be able to graph it.

In 2007, we began working with scientists and teachers in Maine to explore students’ data literacy skills. We found that when students began to organize, graph, and interpret their data, many were unsure about what kind of graph to make. Most made bar graphs, regardless of their research question. They also treated the graph like an end product in itself—instead of using it to see patterns and make argu-ments. Although students had the mechanical skills to gener-ate graphs, they did not logically decide what kind of graph would best suit their particular research question.

Consequently, we developed the Graph Choice Chart (GCC), a tool to help students choose the appropriate graph.

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This article describes the GCC and gives examples of how our partner teachers used it in their classrooms.

BackgroundEarly in our project, we surveyed more than 200 high school students and asked them to draw graphs to illustrate simple comparisons between two groups and the relationships be-tween two variables (Figure 1). In the first part, we asked students to draw a graph to help them determine whether the type of stream bottom—rocky or muddy—affected drag-onfly abundance. The second part asked them to graphically show the correlation between fish size and the concentra-tion of mercury. In the case of the dragonflies, only 23% of students made a graph—a frequency plot or a bar graph of group averages—that visually compared dragonfly abun-dance in the two habitats. In the fish example, only 58% of students correctly made a scatter plot to display the correla-tion between mercury concentration and fish weight. Based on our followup interviews with students, we concluded that, for many, the question “What kind of graph should I use?” did not occur to them.

Thus, the GCC we created takes the form of a decision tree, where a choice at each node, or decision point, leads to other choices, and finally, to an outcome, or type of graph, for each branch (Figure 2, p. XX). This helps students make an informed decision about what kind of graph to use.

Focusing on the research questionThe starting point for the GCC—and a requirement for it to work—is a precisely worded research question. Writing the question forces students to be clear and consistent—and to stick with one question—as they move through their analy-sis. Changing the wording of a question midstream can pro-duce a different kind of graph and cause confusion. In the classroom, our partner teachers find that much of this confu-sion can be resolved by having students reconsider their re-search questions. The process of fitting a graph to a question encourages them to think more deeply about their data as they develop a claim or argument.

Classroom exampleFor example, one partner works with her students to locate bird nests in a forest and measure the distance from each nest site to the nearby lakeshore. After looking at their data table and the bar graphs some draw, students conclude that birds build nests closer to the water because there may be more predators in the deep woods, and thus it is safer by the wa-ter—a conclusion that takes leave of the data and ventures into speculation. The following dialogue demonstrates how the teacher used the GCC to steer her students to a question that can be supported with the data collected:

Teacher: Okay, so what was your research question?Student: Oh… (long pause). It’s about the relationship

between nests and distance to shore. Teacher: How would you word that as a question? Student: Umm…What is the relationship between nests and

distance to shore?Teacher: Okay, what kind of question is that? Use your GCC. Student: (The student studies the chart.) It’s like a correlation

question.Teacher: All right. A correlation question involves two nu-

meric variables. What are the two variables you measured?Student: (Long pause.) We measured distance to the water

and… that’s all.Teacher: So just one variable then. It sounds like maybe you

are interested in what the distribution of nests is with regard to distance to the shore. Just one measured variable (i.e., distance) and one group (i.e., bird nests).

Student: So…(studying the GCC)…a frequency plot! That would show us how the bird nests are spread out in distance to the water.

In this example, the teacher realized that the student had lost track of her question and that prompting her to articulate it and use the GCC to reason through what kind of graph to make might result in a much richer (and clarifying) discussion about the data as evidence. The movement between the question and the graph choice is not unidirectional; thinking about the kinds of data needed for various graphs and the kind of data available enables the student and teacher to move back and forth between the framing of the research question, the nature of the data col-lected, and the kind of graph that might address the actual ques-tion the student has in mind.

The Science Teacher4

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The Graph Choice Chart

FIGURE 1

Examples of high school student comparison and correlation graphs1 a. Dragonfly data graphs.In a survey, students were given a table of data about dragonflies collected from rocky and mucky streams and the following prompt: “Draw one graph showing the data in a way that helps you figure out if the type of stream bottom has to do with dragonfly abundance (e.g., the number of dragonflies).” Seventy-seven percent of students made a graph that did not compare groups.

1 b. Fish data graphs.Students were given a summary of two positively correlated variables and the following prompt: “Draw a graph to display the following data so that you can see if fish size and mercury are correlated. Don’t leave any fish out.” Forty-two percent of students made a graph that did not display a relationship.

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Page 7: Critical Thinking - VAEI · Critical Thinking Critical Thinking is the process of actively evaluating and interpreting ideas. Creative Thinking and Critical Thinking often work together.

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The Science Teacher6

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The Graph Choice Chart

Choosing a graph typeOnce students state their research question, they can use the GCC to identify the type of question they are asking and then link the question type to their choice of graph. The boxes on the left of the GCC are choice-points for identifying the type of question the student is asking (Figure 2). They include:

◆◆ Does your question ask about the variability within a group of data points? (one group, one variable);

◆◆ Does your question compare two or more groups to decide if the groups are the same or different? (two groups, one variable);

◆◆ Does your question ask if two numeric factors are correlated? (one group, two variables); or

◆◆ Does your question ask how a total is proportioned into subgroups? (Or, what proportion a subgroup is of a total?) (one group with subgroups, one variable).

If a student’s question does not clearly fit with any of these choices, the example questions can be used to help the stu-dent rephrase (Figure 2). Once students have identified their question type, they follow the decision-making tree. Students answer the yes or no questions, review the examples for simi-larity to their own questions, and then determine a suitable graph type. (A sample GCC on the question “Has the bloom time of forsythia changed in the state of Maine over the last 30 years?” is available online; see “On the web.”)

Classroom exampleSome of our partner teachers also use the GCC in reverse. For example, using physical data collected by a balloon as-cending through the atmosphere (see “On the web”) teachers ask their students to develop a question that can be answered with these data. Without the GCC, students ask such single-point questions as “What is the average air speed?” “How high does the balloon go?” or “Where did it land?” Students move beyond such questions using the GCC in reverse—starting with different graph types and working backward to see what kind of question might lead to that graph.

For example, students can discuss each question type and then, using the balloon data, write one question of each type on a 3 x 5 card (except proportional questions), with the writer’s name on the back. Students then put their questions in a pile. Each student chooses a question and, again, using the GCC, determines the appropriate graph type to answer that question. If the question is worded so that it is hard to determine the appropriate graph, students ask the writer to explain and rewrite the question.

Refining students’ process Single-number comparisons and variabilityWithout prior instruction, few of our project students make

FIGURE 3

Average kWh data.What was the mean kWh used per month by US households in 2009? (Data source: EIA.gov) The question can be addressed by either a bar graph or dot plot. The dot plot inspires discussion and new questions more than the bar graph does because it shows the variability among the states. (The vertical line in the dot plot is the mean.)

FIGURE 4

Scatterplot.Many high school students inappropriately connect points in a scatterplot. In this case, a ninth grade student connected the dots in the order that they appeared in the data set.

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a frequency plot. Yet, frequency plots are often best when de-termining whether there is a meaningful difference between groups, as in Figure 3 (p. XX), where students explore what the mean kilowatt-hour per month was for U.S. households in 2009. The GCC moves students toward graphical displays of variability when such data are available and the question warrants (e.g., “Which solar car has more consistent race times over ten trials?”) and confines the use of bar graphs to comparisons between single numbers such as mean, median, sum (e.g., “Was total rainfall greater in July or August?”).

Classroom exampleAs previously noted, our early survey work showed that bar graphs were the first choice for many students, regardless of their research question. Teachers using the GCC help stu-dents understand why other kinds of graphs are useful and when to use them.

To explore variability in chromosomes, for example, one teacher gives students a table showing the number of chro-mosomes for a variety of animal and plant species and asks: “Do plant species tend to have more chromosomes than ani-mal species do?”

This teacher finds that students tend to graph these data in one of two ways: They either calculate the average number of chromosomes for each kingdom and plot the averages as two bars on a graph, or they graph every organism as an indi-vidual bar, resulting in a graph with too many bars to enable easy comparison. (See “On the web” for more on this lesson.)

Students typically state that plants have, on average, more

chromosomes than animals, or they find that they cannot make a statement about the groups because plotting all of the data points creates a confusing graph.

The teacher then asks students to use the GCC and con-sider the following: “Does the question ask for a comparison of single numbers that summarizes the two groups, or does it ask for a comparison of groups of data points?” Although students are reluctant to give up the single-number average or any of the individual data points, after a discussion, they often decide that the word “tend” in the research question suggests that they should not reduce these data to an average. Using the GCC, students decide to use boxplots instead.

Once the data are graphed as boxplots, students discuss the graphed evidence with a richness and nuance that cannot emerge from a bar graph. For example, one group said: “There is a lot of overlap, and the median for animals falls within the interquartile range for plants. Perhaps there is no real differ-ence, but the boxplot shows that animals tend to have slightly more chromosomes. The field horsetail and rattlesnake fern are extreme values that really raise the average for plants.”

Correlation and time series We also find that students generally do not consider whether it makes sense to connect data points in an x-y plot. When choosing a graph type to show correlation (e.g., a scatter plot), many students incorrectly connect the dots instead and pro-duce a line graph (Figure 4, p. XX). However, it does make sense to connect data points when students are graphing change through continuous time. To help them make a deci-

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The Graph Choice Chart

sion about when to connect data points, the GCC separates time series from other correlations.

ProportionStudents also tend to incorrectly use pie charts to answer ques-tions about group comparisons or correlations. To help students recognize when pie charts are appropriate, the GCC has a fourth kind of question: questions about proportions of a whole.

Teacher findingsMany partner teachers report that before using the GCC, their students did not know that so many different types of graphs ex-isted. They say that students routinely pull out their GCCs, orig-inally distributed in science class, in their math classes as well.

Teachers also find that students tend to start projects with vague, unformed questions. For example, “My question is about loons” could be: “How do loon populations on Eagle Lake and Moosehead Lake compare?” “Is loon population correlated with lake size?” or “Has the summer loon popula-tion changed through time?” Each question is about loons and yet each warrants a different graph.

Teachers also find that the GCC forces students to work on one question at a time. One teacher uses the motto “one question, one graph” to help students refine a compound question into two single questions. For example, “Does air temperature change more under the trees or in the open and does the difference change through the season?” becomes “How does air temperature change under trees compare with air temperature change in open fields?” (group com-parison) and “How does air temperature difference in two locations change through the season?” (time series).

Another finding is that some students resist the thought-process altogether and simply jump to their favorite graph on the right side of the chart—usually the bar graph—regard-less of their question. To emphasize the thought sequence, one teacher slides a piece of paper over when moving from left to right on the GCC and discusses each “column”  or decision point with students, referring back to the written question before moving along.

ConclusionThe GCC sets up a framework for thinking about data anal-ysis that is based on real questions and reasoning, rather than an absolute set of steps. Feedback from partner teachers who have used the GCC is positive and often enthusiastic. They indicate that students feel empowered when they realize they have a choice about what kind of graph to use.

Over the last several years, we have worked with partner teachers and their students to develop a set of probes and ru-brics for use with the GCC to make formative assessments about students’ proficiency in selecting appropriate graphs. Over the coming year, we will continue to work toward vali-dating and assessing the reliability of these instruments.

The GCC, however, is not perfect. It does not represent hard and fast rules for graphing. But at its core, it helps stu-dents initiate a process of reasoning about graphing based on purpose, rather than on didactic instruction. Once students master linking data analysis to their research question, they can move beyond the GCC and combine options based on reasoned decisions. ■

Hannah Webber ([email protected]) is education projects manager at the Schoodic Institute in Winter Harbor, Maine; Sarah J. Nelson ([email protected]) is associate research professor in Watershed Biogeochemistry at the Uni-versity of Maine in Orono; Ryan Weatherbee ([email protected]) is a research associate in the Satellite Oceanog-raphy Data Lab at the University of Maine in Orono; Bill Zoellick ([email protected]) is education research direc-tor at the Schoodic Institute; and Molly Schauffler ([email protected]) is an assistant research professor in Earth and cli-mate science at the University of Maine in Orono.

AcknowledgmentsThe Graph Choice Chart is part of a larger data literacy framework developed in our Maine Data Literacy Project, which is funded by two Title II Math Science Partnership grants to the Schoodic Institute through the State of Maine Department of Education. We wish to acknowledge the invaluable contributions of our partner teachers as well.

On the webAnimal and plant species chromosomes: http://participatoryscience.

org/data-activity/practice-comparing-groups-chromosome-number-data

Balloon ascent data: http://participatoryscience.org/data-activity/practice-asking-questions-balloon-ascent-data

Graph Choice Chart: http://participatoryscience.org/file/graph-choice-chart

Sample Graph Choice Chart: www.nsta.org/highschool/connections.aspx

ReferencesJiménez-Aleixandre, M.P., A. Bugallo Rodríguez, and R.A.

Duschl. 2000. ‘Doing the lesson’ or ‘doing science’: Argument in high school genetics. Science Education 84 (6): 757–792.

Kilpatrick, J. 1985. A retrospective account of the past 25 years of research on teaching mathematical problem solving. In Teaching and learning mathematical problem solving: Multiple research perspectives, ed. E. A. Silver, 1–16. Mahwah, New Jersey: Lawrence Erlbaum Associates.

NGSS Lead States. 2013. Next Generation Science Standards: For states, by states. Washington, DC: National Academies Press.

Schoenfeld, A.H. 1992. Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In Handbook for research on mathematics teaching and learning, ed. D. Grouws, 334–370. New York: MacMillan.

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