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Jigsaw is a great model of instruction that teaches the students accountability and help them feel like they matter. Students get the opportunity to become the expert on a certain topic and then get to teach a small group about it. They get to become the MKO. As an example of what I could do with this in my classroom, I created a lesson plan. In this, students will be working with different ways of representing a set of data. I think that this would be perfect for jigsaw because I can assign different groups different types of graphs such as histograms, dot plots, box plots, pie chart, etc. They can become an expert on just one of these and then teach this to other groups that haven't learned about that graph yet. Students will be taking notes on the other types of graphs and we can have a brief quiz at the end. This makes each student be accountable for learning their information so that they can teach it to others. I think that this type of cooperative learning could greatly contribute to a complex learning environment for our students.

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In my Secondary Curriculum and Instruction course we had to get into small groups and teach a lesson in our content area using a model of instruction. My group was assigned Inquiry-Based Learning. Attached is our lesson plan for this model of instruction. Essentially, we were teaching a statistics course. We had a pre assessment for our students where we made them find the mean, median, and mode of a random set of data. After this activity, we lead the students into ideas about sampling and generalizations. We gave them definitions of these and gave a few examples. Then we posed an overarching question of "How does sampling from a population help us make generalizations about the population?" This is where the inquiry-based learning really starts to come in. To investigate this question, we had an activity where students would all be looking at packages of m&m's. We had all of our students come up with different questions they wanted answered before opening the bags. These included "On average, how many m&m's are in a package?" or "How many are blue?", etc. Then as a class, we decided to focus on one question together that we want to have answered. We then asked the students to make a hypothesis before opening the bag of what they think the outcome will be. We were looking at the question, on average, how many blue m&m's are in a single package of regular m&m's. We then had each student open up a bag of m&m's and collect their data. So each individual student would count their own bag and then together as a class we would have a larger sample size. Once collecting the data and looking at different aspects of it, such as the mean, median, mode, etc. we came back and looked at their original hypotheses. We asked students to reflect on if it was what they expected, if it was different, and what they would expect if we repeated the experiment. This is how we make generalizations about the population. We talked about how a bigger sample size is more accurate. We had students come to a conclusion about what they noticed about the sample and asked if it would make sense to generalize it back to the whole population of m&m's. We also had the students reflect on this activity and analyze the process. This uses metacognition and will make the learning more memorable for the students. I think that this is a great activity that engages students and lets them explore for themselves more about the topic. We modified our lesson to use m&m's to hopefully get the students more engaged and we let them ask the questions. You could do this with really anything in the math classroom, but I think it's a great tool to have in your repertoire.

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Project-Based Learning is an incredible way to answer the question "When will I ever use this?" It gives students a purpose where they can see real applications of mathematics. In this article, it listed a lot of great ideas. One of which is giving a survey to students at the beginning of the year and building a project around that so that the students are doing something that they actually care about. Well this made me ask myself, "What is one way that every student will use math outside of high school?" And one thing that came to my mind was about buying a house. I could create a project where every student figures out what their future career could be and what their income would be. From here, they could look up on different bank websites what kind of a loan they could qualify for when buying a house. They could look at different terms, rates, down payments, etc. And then they could put it together into some sort of presentation. But this could teach students to use interest formulas such as Pe^rt and others. Students could look on different websites to see what house they would want to buy and then go through the paperwork as if they were actually financing it. I've done assignments similar to this. But I think that making a project where students see actual relevance would be so helpful and engaging (and hopefully they won't ask "Why do I need to learn this?").

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Taking the plunge into project-based learning can seem difficult in an age when standardized testing seems to reign supreme as an indicator of achievement in secondary classrooms. But the pathway to project-based learning doesn't have to be scary for secondary math teachers. Utilizing your own expertise and curriculum materials, you can create projects that are real, relevant, and rigorous, and that answer the age-old question, "When am I ever going to need this?"

Selecting a Project Topic

Project-based learning challenges students to answer or solve real problems in an authentic and meaningful way. The authenticity is key to ensuring that students are invested in the project. One of the best ways to determine what students will find relevant is to survey them. By repurposing the traditional beginning-of-the-year student inventory, you can build in specific questions about students' interests and passions, goals and aspirations. Then, along with keeping an eye on current events, you'll be able to identify relevant topics that can serve as the foundation for a project-based learning experience.

For example, access to the internet has been a long-standing issue in certain communities, and remote learning has highlighted and exacerbated these issues for many of our students. Another timely topic is the spread of communicable disease.

Choosing Appropriate Math Content

Determine the suitable math content to connect with the topics you've chosen. While not every content standard is an appropriate standard for a project, it's important to consider the domain of rigor for the standard (applicable, conceptual, procedural), as well as the role of the standard within a curriculum. Prioritizing standards that meet a combination of applicable rigor, Common Core modeling standards, and/or Widely Applicable Prerequisites (WAP) standards will ensure that you're utilizing standards that are rich in opportunity for deep learning throughout the project process.

With the internet-access issue, students in geometry class can use circles and coordinate geometry overlaid on maps of their city or town to analyze cell service in rural and urban areas to address the digital divide and connectivity issues within their community.

For the spread of disease, functions provide a great background on which to build a project-based learning unit. Functions model relationships between variables and are useful for designing projects around communicable diseases like the cold, the flu, or Covid-19 and how to slow or stop the spread through analyzing data and modeling with exponential functions. You can design projects around data analysis and modeling of spread using actual data from the real world or simulate the spread of germs in the classroom or school building using glow powder, and collect data from the simulation.

Project-based learning gives you the opportunity to represent problems algebraically (through creating equations, writing functions, graphing, and analyzing graph features). Help students discover the complexities of credit and loans when preparing plans for financing their future by bringing algebraic exponentials and rationals to life through the study and application of financial formulas.

Planning the Project

When designing your project, your textbook or curriculum can serve as a great anchor, providing students with familiar resources and structures for acquiring mathematical content knowledge and skill practice.

It's helpful to break the project down into manageable chunks, or milestones, each with its own driving question. Use these driving questions to determine the best content from your curriculum to include within that milestone. You can then select the appropriate lessons and practice assignments from your curriculum that will support the students' learning, but be prepared that it may alter the order in which you teach some of the lessons.

Including Test Prep

In addition to the inherent elements of critical thinking that arise within each project-based learning experience, there are clear connections between projects and preparation for standardized assessments, such as the SAT.

Incorporate skills from the "Problem Solving and Data Analysis" section of the SAT Study Guide, directly within a project through project launches, where data is presented and discussed to elicit critical thinking, reasoning, and sense making as students develop their need-to-know questions. Focusing on data relevant to the project through daily or weekly data talks provides additional opportunities for students to practice these reasoning skills.

Additionally, you can focus on associated topics from the "Heart of Algebra" and "Passport to Advanced Math" sections of that study guide. Project-based learning provides the lens to view the algebra contextually, giving you the opportunity to support students in representing the problems algebraically (through creating equations, writing functions, graphing and analyzing graph features). For projects with a focus on geometry or trigonometry, you can make direct connections to the " Additional Topics in Math " section through geometric modeling and analysis and problem-solving with trig or complex numbers, as appropriate.

We have the ability to use our expertise and our resources to provide authentic and engaging project-based learning experiences within our secondary math classrooms. There are many possible projects-analyzing the geometry of packaged goods and recycling statistics to determine the environmental impact and proposing more sustainable alternatives, or using systems of equations to analyze time and budget constraints to better determine student lunch options. Because of these rich project-based learning experiences, ultimately it will be not the teacher but the student who has the answer to the age-old question "When am I ever going to need this?"

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Creating Opportunities for Project-Based Learning in Math

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Taking the plunge into project-based learning can seem difficult in an age when standardized testing seems to reign supreme as an indicator of achievement in secondary classrooms. But the pathway to project-based learning doesn't have to be scary for secondary math teachers.

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I was having a really hard time coming up with an idea that I could do in my math class for Service-Learning. I found this article and it talks about how there aren't as many opportunities to do this in a math class as there are in other contents. However, that doesn't mean it's not possible. This article listed a few ideas such as tutoring or creating a math fun fair. I think that these are both great ideas that could really get my students engaged in their learning. With tutoring, that would probably be more realistic if doing it in an honors or higher level math class. But I could have my students be paired up with someone from a lower grade level and they could apply what they have already learned to help the younger students. I think that this could help build student confidence as they become MKOs and feel like the expert. But it could also encourage and motivate them because they are using what they have learned to help someone else. And I know it depends on what school I work at and what the rules are but maybe I could have my students help me put on a math fun fair where we could raise money for a certain cause and put on like a carnival that involves different math games. One game that I think could be fun is angry birds. I've done an activity with this where you work with equations of curves and you try to come up with the best equation and then put your equation to the test by launching water balloons at stuffed animals following the equation that you have created. There's a ton of other games you could have at this as well. But just have the students run booths and come up with different games that could be fun for others. These are both great activities where students can take what they've learned and engage in helping others with it.

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Service-Learning and Making a Difference

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a guest post by Karl-Dieter Crisman Crisman at the 17th Annual Legacy of R. L. Moore—Inquiry-Based Learning Conference (photo Kirk...

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Technology-enhanced learning environments does an incredible job at getting students involved especially in the world that we live in today. A source that I've been introduced to and that I want to use with my students is called CODAP. I've linked an article kind of explaining what CODAP is and how it's useful. On here, you can create/collect data and put them into so many different graphs, tables, pictures, etc. It helps students visualize and compare data in a quick and easy manner. It might take a little while for students to get a hang of how to use CODAP, but once they do, it's a great tool for them to actually understand what the numbers represent in a set of data and how they compare to another piece of the data. This can quickly calculate things such as the linear regression line, box plots, IQR, etc. This is a really cool tool that I wish I would've had when I was in high school and I think it would make a great use of technology to get my students more engaged and contribute to a complex learning environment. Below is a link to a set of data from CODAP that you can play around with.
https://codap.concord.org/app/static/dg/en/cert/index.html#file=examples:Mammals

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Importance

Data are everywhere. Just as language and numeric literacy involve understanding the world through words and mathematical constructs, data literacy involves understanding the world through data exploration. Today's middle and high school students need to work with data in order to advance their skills and prepare for the burgeoning careers and inquiry-based practices of data scientists.

CODAP provides an easy-to-use web-based data analysis platform, geared toward middle and high school students, and aimed at teachers and curriculum developers. CODAP can be incorporated across the curriculum to help students summarize, visualize and interpret data, advancing their skills to use data as evidence to support a claim.

Through research on learning, collaborative software design, web application development and user testing, we're developing a Common Online Data Analysis Platform (CODAP) that will serve subsequent curriculum development projects as a basis for the technology with which students engage with data.

CODAP is open source software, free to use, adapt and extend.To increase the likelihood that CODAP software will meet the needs of a wide range of curriculum projects it is being designed and tested in collaboration with four existing NSF-funded projects: Building Models, Data Science Games, InquirySpace, Ocean Tracks, Terra Populus, Enhancing Statistics Teacher Education with EModules (ESTEEM), and Zoom In! Learning Science with Data. These projects form the nucleus of a community of developers that will grow with time and lead to widespread use of CODAP's data exploration and visualization tools in middle and high school classrooms across a variety of subject areas.

Teachers: Learn more about using CODAP "

Research

We're researching the ways students perceive and learn to work with empirical data that's structured hierarchically. Our goals are to add to the field of data science education and to improve the design of data analysis learning environments.

Videos

View all these videos and more on the Concord Consortium YouTube Channel.

Publications

Finzer, B., & Wilkerson, M. (2020). Writing data stories. @Concord, 24(1), 10-11.

Finzer, B., & Kochevar, R. (2019). Monday's lesson: Zoom in! teaching science with data. @Concord, 23(2), 7.

Finzer, W., Busey, A., & Kochevar, R. (2018). Data-driven inquiry in the pbl classroom: Linking maps, graphs, and tables in biology. The Science Teacher.

Konold, C., Finzer, W., & Kreetong, K. (2017). Modeling as a core component of structuring data. Statistics Education Research Journal.

Finzer, W., & Damelin, D. (2016). Design perspective on the common online data analysis platform (codap). Paper presented at American Educational Research Association (AERA) conference, Washington, D.C..

Finzer, W., & Damelin, D. (2015). Building theCODAP community. @Concord, 18(1), 16.

Finzer, W., & Tinker, R. (2015). Under the hood: Embedding a simulation inCODAP. @Concord, 19(1), 14.

Finzer, W. (2014). Hierarchical data visualization as a tool for developing student understanding of variation of data generated in simulations. in proceedings of the ninth international conference on teaching statistics (vol. 6). voorburg: International statistics institute.

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Software

CODAP is easy to use and runs in your web browser. Open an example document or create your own by dragging in a CSV or TXT file and start bringing data to life!

The CODAP project uses IntelliJ IDEA as part of its software development process.

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Common Online Data Analysis Platform (CODAP) provides an easy-to-use web-based data analysis platform that can be incorporated across the curriculum to help students summarize, visualize, and interpret data, advancing their skills to use data as evidence to support a claim.