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K-12 Math Projects:
About Project-Based Learning

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Project-based learning is a terrific way to link your curriculum with real world events and applications of concepts that your students are learning.  There are two pages in this section to help you and your learners:

Arrow: You are hereProject Based Learning (Page 1 of 2): An essay

Projects on the Web (Page 2 of 2): Our list of project sites

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About Project-Based Learning

 

Among the greatest benefits of project-based learning (PBL) are gains in students' critical-thinking skills and development of their interpersonal and intrapersonal skills.  PBL is also an ideal way to help learners gain speaking and presentation skills indentified in the Common Core Standards. PBL in mathematics, particularly when completed in teams, helps learners "model with mathematics" as they  "apply the mathematics they know to solve problems arising in everyday life, society, and the workplace,"  "use tools strategically,"  and "construct viable arguments and critique the reasoning of others," as noted in the Common Core Standards (2010) for Mathematical Practice.

However, as Bryan Goodwin (2010) found in reviewing the literature, a major shortcoming in many student projects is that educators tend to assign projects just for the sake of doing them.  "Educators can avoid this phenomenon and realize the potential of projects to promote students' critical-thinking by framing projects around a driving question" (p. 81).  This driving question is just one of eight essential elements of meaningful projects, according to John Larmer and John R. Mergendoller (2012, 2010) of the Buck Institute for Education.  Every good project needs significant content.  Students also need to perceive the work as meaningful to them.  A clear connection to an entry event adding this meaning might be via almost anything: "a video, a lively discussion, a guest speaker, a field trip, or a piece of mock correspondence that sets up a scenario" (2010, p. 35).  Students need a voice and choice in fulfilling project requirements, keeping in mind that limited choices be considered and that "teachers should design projects with the extent of student choice that fits their own style and students (p. 36).  Projects should give students opportunities to build 21st century skills and to use technology that will be useful to them in life and the workplace.  Projects should enable learners to conduct real inquiry, as with "real inquiry comes innovation--a new answer to a driving question, a new product, or an individually generated solution to a problem" (p. 37).  Learners should receive feedback to use in revision, as learning that real-world work often involves revision.  Finally, students should publicly present their work, as they will be more motivated to produce a quality product when knowing a real audience will view it.

With the above being said, Volker Ulm (2011) offered teachers some sound advice regarding math project-based learning:

Enriching classroom teaching with projects is certainly the most challenging, but at the same time the most beneficial form of independent learning. It is challenging because it requires high-level skills on the part of the students, e.g. skills in applying methods, self-management, and social competence. So project-based learning should never degenerate into a teacher-centered training course where ultimately the teacher still does all the planning, structuring and organizing, prepares and procures all the materials, or even produces and presents the results. (p. 44)

What do we mean by building 21st century skills?

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Numerous documents have referred to the need for this or that activity to build 21st century skills needed for career and college readiness.  However, what does that mean stated in terms that everyone can easily remember?

The National Research Council (2012, p. 2) suggested three broad domains as a way in which to organize competencies--such skills and abilities: cognitive, intrapersonal, and interpersonal.  They are intertwined based on human development and learning, however.

While one might elaborate on specific skills or competencies within each, those domains are easy to remember.  Briefly:

  • the cognitive domain includes thinking, reasoning, and related skills;
  • the intrapersonal domain involves self-management, including the ability to regulate one’s behavior and emotions to reach goals;
  • the interpersonal domain involves expressing information to others, as well as interpreting others’ messages and responding appropriately. (p. 2)

What might not surprise readers, however, is that "Precise definitions of the many terms used for “21st century skills” are not possible at this time, in part because there is little research to support such definitions" (p. 2).

 

Key Questions

Thus, projects should result from students' attempts to answer essential questions.  They can take many forms: products, presentations, performances.  They might fit any of three structures: interpersonal, information sharing, or problem-solving.  When selecting an existing project, or creating one of your own, consider the following.  In terms of math projects:

  1. Is the project devoted only to mathematics (or a single subject area), or is there a link to other curricular areas?

  2. Is the project tied to standards for the curricular areas addressed, such as those from the National Council of Teachers of Mathematics and the National Education Technology Standards?

  3. Does the project come with classroom instructional materials (e.g., teacher resources, student activities, rubrics and assessment tools)?

  4. Can all students in your class participate? Projects should not be reserved for your talented and gifted students, as all students should be able to benefit.

  5. What is the total time for project completion?

  6. Is the project collaborative in nature? A collaborative project, particularly involving students outside your own school setting, will take more time and monitoring to help students learn how to be a part of a team and communicate appropriately with others.

  7. How will students benefit both academically and personally from their involvement in the project?  Consider that when students interact with other students and experts across the country or internationally, they get a broader feel for diversity.  Their participation in an actual real world activity might encourage them to do their best work, and see the relevance of mathematics in their daily lives.  If students have input into project selection, and like the topic, they will tend to become more involved and excited about their learning.

  8. Is there a cost involved to participate?

Adding to the above, educators need to decide on what they mean by project-based learning (PBL) and which model is needed.  In his book World Class Learners: Educating Creative and Entrepreneurial Students, Yong Zhao noted three forms of PBL, according to J. Robinson (2013).  In an academic model, all elements are controlled by the teacher.  The goal is to teach prescribed content and skills.  Products are not meant for authentic consumption.  In a mixed model of PBL, the artifacts students create (sometimes for consumers outside of school) and prescribed content are valued.  Still under the control of the teacher, students have a degree of freedom within the project.  The focus is more on learning real world skills, rather than transmitting knowledge.  Both of these latter models are about teaching the curriculum.  The third PBL method is a product-oriented Entrepreneurial Model, which is the most valued for developing 21st century skills and an entrepreneurial mindset.  Students who work individually or collaboratively are more in control of products, which must meet an authentic consumer need.  Students develop a business plan and the teacher takes on the role of consultant.

The Methodology

These resources are for those who need to know more before engaging in projects and inquiry based learning.

Designing Learning is a section within the Galileo Educational Network Association, which includes a series on the nature of inquiry-based learning.  Learn about what inquiry is all about, choosing a topic, essential questions, inquiry and assessment, and then go to the section for Classroom Examples of projects for elementary, middle,  and secondary students and a rubric for assessing inquiry projects.

Intel Education has a three-hour hands-on free workshop on project-based learning, which has a guided self-study module as an accompaniment.  Learn about this method as you examine It's a Wild Ride, an extended interdisciplinary project that studies roller coaster design in science, mathematics, and language arts classrooms.  It's a Wild Ride provides a case study experience.  Intel then offers a series of K-12 projects categorized in mathematics, science, language arts, social studies, and interdisciplinary.

PBL-Online has all the resources you need to design and manage high quality projects for middle and high school students.  You can learn how to design your own project, what project based learning is all about, search for projects developed by others or contribute your own, review research on PBL, and access other web resources on the topic. PBL-Online was created under the leadership of the Buck Institute of Education, with major contributions from the George Lucas Foundation and others.

HOT: Project-Based Learning: A Resource for Instructors and Program Coordinators from the National Academy Foundation and Pearson Foundation provides comprehensive coverage on this topic.  You'll find a definition of PBL, questions to consider for when to use PBL, conditions and research supporting PBL, PBL examples and links to resources and training.  Commentary on PBL includes: "The best projects skillfully weave together opportunities for students to engage in classroom activities (Level 1) that address content standards (Level 2) while encouraging them to develop habits of mind (Level 3) and the ability to take responsibility of their own learning (Level 4)" (p. 12).  The 6 A's of PBL are addressed: Authenticity, Academic Rigor, Adult Connections, Active Exploration, Applied Learning, and Assessment Practices.  Finally, within Project Delivery you'll learn about the scaffolding that teachers must consider when implementing sophisticated projects in their classrooms.

Project-Based Learning Professional Development Guide at Edutopia.org from the George Lucas Educational Foundation can be used as a two- to three- hour learning module, or expanded to day-long workshops.  Find out what project based learning is, why it is important, how it works, and get some supporting resources.  Also see Edutopia's Project-Based Learning section.

Project Based Learning explained by Common Craft is a short video with an easy explanation of PBL, courtesy of BIE.org.

Project Approach to Teaching and Learning in school addresses the foundation theory for using projects, strategic planning, and project development structure.  This is an award winning site by Sylvia Chard of the University of Alberta, Canada. You might also be interested in the interview of Dr. Chard addressing project-based learning, which is available from Edutopia of the George Lucas Educational Foundation.

In Using the Internet to Promote Inquiry-Based Learning, authors D. Jakes, M. Pennington, and H. Knodle describe a structured approach to inquiry-based learning that uses the World Wide Web.  They address an intuitive 8-step process that begins with an essential question and ends with a knowledge product produced by students, typically completed in a cooperative setting. They discuss the skills that students and teachers require to make inquiry-based learning and the Internet a successful endeavor; and the components of a Project Page, which include the scenario, task, resources, product students will build, and assessment.

 

Learn More on Project-based Learning in Middle Grades Mathematics

Yetkiner, Z. E., Anderoglu, H., & Capraro, R. M. (2008). Research summary: Project-based learning in middle grades mathematics. Available from http://bie.org/object/document/pbl_in_middle_grades_mathematics 

 

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Design Your Own Math Project or WebQuest

 

Do you need project ideas?

Volker Ulm (2011) had several ideas for potential math projects.  Selection, of course, depends on the skills of your learners for meaningful project-based learning:

Do you want learners to design their own math project?

There are multiple tools in a variety of categories on the Web for project-based learning activities.  Deal (2009) included specific examples within categories such as collaboration suites, course management systems, dedicated project management tools, wikis, web-conferencing tools for real-time communications, collaborative concept mapping tools, presentation and slide sharing tools, online collaborative writing tools, and task management tools.  The choice would depend on the objectives of the assignment and whether or not the project is to be completed by individual learners or collaboratively within groups.

If you are planning your own project, consider:

Bubble.us is a free web application that allows groups to brainstorm online and create mind maps.  You can embed the map in a blog or website, or save the mind map as an image.  This is a great way to start projects.

Buck Institute for Education has an overview of project based learning (PBL), plus numerous resources for conducting PBL, which are "organized into three broad categories: things to read, to watch, or to interact with."  A PBL handbook and other PBL books are available to purchase.

ClockingIT provides free space for project management, collaboration, and time and task management.

Glogster EDU provides a secure space online for educators and their learners to have an outlet for their creative posters or glogs.  A glog is a virtual online poster that incorporates multimedia.  In addition to text, learners can embed images, audio, video and hyperlinks.  Posters are great projects for students to illustrate what they have learned.  You'll find many examples of student glogs for math at this site to give you ideas.  The site is free.

Wikispaces for Education enables free, private, and secure collaborative group work in classrooms.

What is a real WebQuest?

Web Quest GifConsider a WebQuest, an inquiry-oriented activity in which most or all of the information used by learners is drawn from the Web.

Math WebQuests help students to develop reasoning and critical thinking skills, as advocated in the process standards of the NCTM Goals 2000.

 

According to Tom March (2003) in The Learning Power of WebQuests, there are six elements of a real WebQuest:

  1. a scaffolded learning experience,
  2. use of links to essential resources on the World Wide Web,
  3. an authentic task to motivate students' investigation,
  4. open-ended questions,
  5. development of individual expertise, and
  6. participation in a group process that transforms newly acquired information into a more sophisticated understanding.

Some activities may be designed to use Internet resources to produce a product, but can't be classified as WebQuests.  These non-Webquest activities are those that enable learners to gather  information that can go from a browser directly to a product without altering or involving students' understanding, and reflection on their own metacognitive processes.  To assess the real value of a WebQuest, ask "Is this WebQuest real, rich, and relevant?"

Webquest Tutorials, Templates, and Project Examples

Creating a WebQuest: It's Easier Than You Think! from Education World

Tom March/ozline.com Tom March, one of the original developers of WebQuests, has his own site with his blog, numerous articles and examples of WebQuests.

WebQuest.org training materials.  This site is maintained by Bernie Dodge, who with Tom March developed this model at San Diego State University in 1995.

WebQuest 101 from TeachersFirst.com will help you get started.

WebQuest Template from Cape Breton-Victoria, Regional School Board, Education Centre.  Includes directions within the sections: Introduction, Task, Process, Evaluation (Rubric design), and Conclusion.

Free ResourceHOT: Zunal WebQuest Maker is free web-based software for creating WebQuests in a short time without writing any HTML codes."  The site includes 100 templates.  You can include unlimited files and pictures, embed video, add a pre-test and post-test, create a quiz, add a table/rubric, and more.  A bonus is shared webquests in multiple content areas to use or give ideas for designing your own webquest.

 

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Project Assessment

 

Check mark for project assessmentIf you decide to create your own project, including one that might involve multimedia, assessment will play a key role.  If the nature of your project is collaborative, Ashley Deal (2009) noted that three areas can be assessed.  "Instructors can evaluate the process students use in approaching a given problem and finding solutions; they can assess the final product or end result of the project; or they can evaluate the individual student’s learning outcomes" (p. 4).  However, a single approach to assessment of group work poses a problem, as "a satisfactory final product does not necessarily indicate that students approached the problem according to the preferred process. Similarly, even using the correct process to arrive at a satisfactory final product does not indicate that individual students grasped relevant concepts" (p. 4).  So, more than one level of assessment is recommended.

Learn how to create rubrics to help measure quality and student performance on projects with these additional resources. Or, use an existing rubric.

The following existing rubrics from various locations might be of value in projects:

Teach-nology's Rubric Makers allow you to make grading rubrics by filling out a simple form. The materials are made instantly and can be printed directly from your computer.  You can also customize your own rubric.  Rubrics of interest include homework, class participation, math projects, oral presentations, WebQuests, team work, writing, research reports, and reading.

The Scoring Guide for Student Projects is also an excellent resource developed at the North Central Regional Educational Laboratory (MCREL).  This Web tool helps teachers evaluate student products that are created with technology. It focuses on the student’s content knowledge and effective technology use.

Student Checklist and Judges' Rubric from Multimedia Mania, which is an annual award program sponsored by ISTE HyperSig.

 

Help your students to understand the beauty of mathematics found in nature.

Often students have difficulty seeing the math that is around them everyday or they lack motivation for studying mathematics because they don't see the connection of it to everyday life.  One way to help them is to show them the beauty of math found in nature.  These can also provide great topics for projects.

Fibonacci series and Golden Ratio image View the short video, Nature by Numbers, created by Cristóbal Vila, which was inspired by numbers (e.g., Fibonacci and Golden Ratio), geometry, and nature.  This is truly beautiful and eye-opening.  Then visit:

  • Dr. Ron Knott's web site contains more on Fibonacci numbers and the Golden Section in nature.  You will also find activities to do with your learners. Note: The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next).

  • Fibonacci imageWho was Fibonacci?  Fibonacci or Leonardo of Pisa lived from 1170-1250.  Read a "brief biographical sketch of Fibonacci, his life, times and mathematical achievements."

  • Golden Ratio is about 1.618 and is given the Greek symbol "phi."  Math is Fun provides learners with an easy to understand explanation of the Golden Ratio, the Golden Section, and Fibonacci numbers.

  • Learn more about the golden ratio at GoldenNumber.net and see where it is used in everyday applications.

  • The image of the Fibonacci series shown is from Flawlesslayout.com within a post called Flawless Layout Logo, the Golden section proportion and the Fibonacci series formula where you'll find more images of the golden section in nature.

The Exploratorium in San Francisco features the Geometry Playground, which will change how you view geometry in nature.  It contains three sections: The Geometry of Seeing with a photo exhibition of the invisible geometry of light; The Geometry of Moving on the arcs, angles, and shapes created when people and things are in motion; and the Geometry of Fitting Things Together.  Each includes hands-on activities for grades K-8.  The Geometry Garden features curiosities found in nature from crystals to seashells to sculptures.  The site was made possible by the National Science Foundation and the Gordon and Betty Moore Foundation.

 

Learn about fractals.

Water FractalThe PBS television series , NOVA, has a one-hour program about fractals called Hunting the Hidden Dimension. There are five chapters, which can be viewed separately.  Learn about fractals in nature, including those in the human body.  There are links and books, a teacher's guide, and an email newsletter for learning more.  You can also design your own fractal using NOVA's interactive generator.

Fractal Keys: A Pattern Paradise from the MathScience Innovation Center is a must see site for an adventure into learning all about fractals and where you can find them--everywhere, including music!  Learners in grades 5-12 will benefit.  Begin by clicking on the Welcome Center and viewing What are fractals?

Explore fractals with this unit by Cynthia Lanius, which is appropriate for elementary and middle schools learners and even adults.  You will learn about the importance of fractals, properties of fractals, create a few, and get a series of links to other sites on the Web that address this topic.

NCTM Illuminations Fractal Tool applet, designed mainly for middle school learners, is a virtual manipulative to see how various shapes are fractals.  Users can play with shapes that grow, shrink, and change over several stages and explore self-similarity and patterns in fractal measurements.

Fern Fractal Amazing Seattle Fractals! will benefit high school learners and above.  The developer provides tutorials to learn more about fractals and how to create fractal art.  Users can download free fractal software programs and view some fractal art galleries.

If you wish to generate 2D or 3D fractals and those with animation, consider ChaosPro, which is freeware for MS Windows.  It includes tutorials and a gallery of examples.

Pomegranate Software offers the program called Fractals, which is designed for use on iPad, iPhone, and iPod Touch.  It “renders as you move and pinch to explore Mandelbrot and Julia set fractals in real-time.”  See the exciting displays and learn more about fractals at this site.

 

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References

Common Core State Standards. (2010). Standards for Mathematical Practice. Retrieved from http://www.corestandards.org/Math/Practice

Deal, A. (2009). Collaboration tools.  Carnegie Mellon University.  Retrieved from http://www.cmu.edu/teaching/technology/whitepapers/CollaborationTools_Jan09.pdf 

Goodwin, B. (2010). Choice is a matter of degree. Educational Leadership, 68(1), 80-81. Retrieved from http://www.ascd.org/publications/educational-leadership/sept10/vol68/num01/Choice-Is-a-Matter-of-Degree.aspx

Larmer, J., & Mergendoller, J. R. (2010). Seven essentials for project-based learning. Educational Leadership, 68(1), 34-37. Retrieved from http://www.ascd.org/publications/educational_leadership/sept10/vol68/num01/Seven_Essentials_for_Project-Based_Learning.aspx  See the 2012 update: 8 Essentials for project-based learning at http://bie.org/object/document/8_essentials_for_project_based_learning

March, T. (2003). The learning power of webquests. Educational Leadership, 61(4), 42-47.

National Research Council (2012, July). Education for life and work: Developing transferable knowledge and skills in the 21st century [Report Brief]. J. W. Pellegrino, & M. L. Hilton (Eds.); Committee on Defining Deeper Learning and 21st Century Skills; Center for Education; Division on Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Retrieved from http://www.nap.edu/catalog.php?record_id=13398

Project Based Learning. Buck Institute for Education.  Retrieved from http://www.bie.org/

Robinson, J. (2013, May 27). From the principal's office: Which model of project-based learning is needed? [Web log post]. Retrieved from http://www.techlearning.com/Default.aspx?tabid=67&entryid=5869

Ulm, V. (2011). Teaching mathematics - Opening up individual paths to learning. In series: Towards New Teaching in Mathematics, Issue 3.  Bayreuth, Germany: SINUS International.  Retrieved from http://sinus.uni-bayreuth.de/2974/

 

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