Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
Project-based learning is a terrific way to link your curriculum with real world events and applications of concepts that your students are learning. These resources will:
Inform you about project based learning, including key questions and the methodology
Link you to projects on the Web
Help you and your students to design your own curriculum-based multimedia projects, including WebQuests
Help you assess projects, including those involving multimedia.
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 seven essential elements of meaningful projects, according to John Larmer and John R. Mergendoller (2010) of the Buck Institute for Education. In every good project, 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" (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, thus 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) offers 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?
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:
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).
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:
Is the project devoted only to mathematics (or a single subject area), or is there a link to other curricular areas?
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?
Does the project come with classroom instructional materials (e.g., teacher resources, student activities, rubrics and assessment tools)?
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.
What is the total time for project completion?
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.
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.
Is there a cost involved to participate?
Math projects don't have to be big.
Connect them to real-life events.
REALLY HOT: Bridges Inspire your students to be creative in a project connecting art to mathematics. Visit the Bridges Galleries where you will find numerous mathematical art exhibits, photos, and a virtual museum with creations (e.g., paintings, drawings, sculptures, spherical art, origami, prints, textiles) by mathematicians and artists who are mathematically inclined.
HOT: TheFuturesChannel.com contains videos that link math and science to real world applications and careers. For example, the section on Teaching & Learning contains Algebra in the Real World (by topics covered within a typical algebra course), Hands on Math (by strands), Problem Solving (by strategies), and more. Each video is accompanied by a lesson that delves into the video's content. Best of all, videos and classroom activities are free.
HOT: NASA Online has award winning science, math, and technology videos organized by grade bands: K-2, 3-5, 6-8, 9-18. Many are accompanied by instructional materials and interactive activities. For example, NASA Connect is "an inquiry-based and standards-based, Emmy® award-winning series of mathematics-focused, instructional programs for students in grades 6 - 8. The series includes a 30-minute instructional broadcast, a companion lesson guide, and an interactive web-based application." The learning modules include math simulation videos--short clips showing how algebra and geometry topics in ratios, percents, and graphing apply for gravity (Earth vs. Moon, Earth vs. International Space Station), auroral activity, Mach speed of airplanes, and balancing a teeter-totter. There's also one showing how a parabola and its equation relates to basketball.
See the short video Using Parabolas in Real Life at YouTube. Students analyzed parabolas found in real world--like the famous McDonald's golden arches.
HOT: Math teacher Thomas Petra has a terrific site, RealWorldMath.org, that integrates Google Earth and SketchUp into the math curriculum. He stated, "Within this site you will find lesson ideas, examples, and downloads for mathematics that embrace active learning, constructivism, and project-based learning while remaining true to the standards. The initial focus will be for grades 5 and up, but teachers of younger students may be able to find some uses or inspiration from the site. Higher level thinking skills, such as analysis, synthesis, and creativity are encouraged as well as technology skills and social learning. The core of this site is mathematics, but many lessons lend themselves to interdisciplinary activities also." (About this site section)
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The Amazon widget below shows books using the search phrase: project based learning. You can also use the widget to search with other key words. Suggestions include:
These resources are for those who need to know more before engaging in projects and inquiry based learning.
Inquiry and Information and Communication Technologies from the Galileo Educational Network Association 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 get classroom examples of projects for elementary, middle, and secondary students and a rubric for assessing inquiry projects.
Intel® Innovation in 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.
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.
Project Based Learning is a two- to three- hour learning module at Edutopia.org from the George Lucas Educational Foundation. Find out what project based learning is, why it is important, how it works, and get some supporting resources.
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.
Yetkiner, Z. E., Anderoglu, H., & Capraro, R. M. (2008). Research summary: Project-based learning in middle grades mathematics. Retrieved from http://www.nmsa.org/Research/ResearchSummaries/ProjectBasedLearninginMath/tabid/1570/Default.aspx
If you wish to become involved with project-based learning, it might be easier to start by participating in one or adapting one to your setting that has been designed by others.
Ask Dr. Math is an e-mail questioning and answering service for math students and their teachers. Dr. Math also gathers the best questions and answers into a searchable archive organized by grade level (elementary, middle school, high school) and topic (exponents, infinity, polynomials, etc.).
CAMS (California Academy of Math and Science) Inventors Inc. Successful Investor Project is designed to give high school seniors firsthand knowledge of the world of entrepreneurship. The project can encompass one full academic semester or an entire year, and it is broken down into five sections:
Questions on investments, and an individual investment portfolio
Entrepreneurship time (developing a business plan to market a product)
Time to invest (stock market research, selection, and tracking
The convention (a business convention where students display their business plan and product, with marketing and advertising)
Wrapping up the project (debriefing)
CIESE, the Center for Innovation in Engineering and Science Education, sponsors and designs projects for elementary, middle, and high school students that utilize real time data available from the Internet, and global collaboration with peers and experts. Each project has a brief description and links to the National Science Standards and NCTM math standards it supports. All focus on science and mathematics, but have many interdisciplinary aspects as well, including social studies, language arts, art, and foreign languages. See the Math and Science Projects at http://www.ciese.org/mathprojects/. Projects have received accolades from the U.S. Department of Education, Discovery Channel, the National Science Teachers Association, and more. Extensive teacher resources are available to support technology integration, professional development, and Internet safety. Links to Real Time Data Sites are particularly useful.
Data Library from the Math Forum contains lists of on-going data-sharing projects as well as downloadable Excel and Clarisworks spreadsheets along with other sources of data on the web.
Electronic Emissary from the University of Texas connects your students to projects involving professional experts and uses e-mail for mentoring. The project went online in 1993 and is believed to be the longest-running Internet-based telementoring and research effort serving K-12 students and teachers around the world. Project-based online conversations typically range in length from 6 weeks to a full academic year, as students' needs and interests dictate.
ePals can be your portal to a global community. Schools and districts can join for free to safely connect, collaborate and learn using protected email and blog solutions. There are several existing projects, plus online forums for teachers, students, family, and projects.
eLanguages "is a global online community of teachers sharing ideas and working together with their students on curriculum relevant projects." Join an existing project or start your own. "eLanguages is flexible and can support activities in all subject areas across the whole age range" (What is eLanguages? section). The site is free and available in over 20 languages.
Global SchoolNet has a Projects Registry of more than 2,500 annotated listings of teacher-led global projects. It is searchable by date, age level, geographic location, collaboration type, technology tools used, or keyword. Narrow your search also by curriculum area. Join an existing project or announce one of your own. The database has several hundred projects addressing math.
GLOBE (Global Learning and Observations to Benefit the Environment) is a worldwide hands-on, primary and secondary school-based science and education program. Students use the scientific method to create hypotheses, analyze data, draw conclusions and report their results through the Internet. They take scientifically valid measurements in the fields of atmosphere, hydrology, soils, and land cover/phenology - depending upon local curricula. GLOBE trains teachers to help students improve their achievement in science and math, and in the use of computer and network technology.
Hands-On Math Projects, Volume 2, by Carolyn S. Carter with Sara Cohen, Marian Keyes, Patricia S. Kusimo, and Crystal Lunsford (2002), contains two chapters devoted to "Projects That Help Middle-School-Age Youth Discover the Science and Mathematics in Everyday Life." The Mathematics of Quilting exposes learners to plane geometry, symmetry, and tessellations. In Making Art through Mathematics, learners explore Cartesian coordinates, 2-D and 3-D geometry, measurement, symmetry, and volume. This is a pdf document.
iEARN (International Education and Resource Network) "enables young people to use the Internet and other new technologies to engage in collaborative educational projects that both enhance learning and make a difference in the world." Math projects, for example, include Mathematics and Agriculture (ages 10+), Connecting Math to Our Lives (all ages), and Mathematics Virtual Learning Circle (all ages). iEARN offers both face-to-face and online professional development workshops and courses for educators seeking to integrate online global project work into their classrooms. Workshops include the technical, collaborative and organizational skills needed to participate.
Los Angeles County Office of Education, Center for Distance and Online Learning, has numerous subject matter resources, classroom projects (completed and ongoing), computer technology resources (e.g., lesson plans, webquests), teacher tips, standards/assessment documents, and more. Definitely worth the look.
Making Mathematics includes open-ended research projects suitable for grades 7-12, which was supported by a grant from the National Science Foundation during 199-2002. Math projects, which remain online for replication, are rated from 1 (no algebra) to 4 (advanced algebra and beyond). Projects contain the problem statement, prerequisites, warm-up problems, hints, resources, teacher notes, extension problems, results. Additional resources include a teacher handbook with advice and activities for teaching research skills, a mentor handbook, and mathematics tools with important supporting content regarding proof, number theory, Pascal's triangle, Geometry of complex numbers, Iteration, and Numbers and Infinity.
MathMovesU is an initiative from Raytheon Company to make math more interesting for middle school students. MathMovesU.com, middle school students can enter a "virtual world" of math and engage with games, polls, flash cards, word problems, and factoids all centered on their passions: music, sports, and fashion. Students earn points for bragging rights and can enter sweepstakes to win prizes. The MathMovesUniversity section of the site features a glossary of math terms and a large number of hands-on worksheets for students looking for additional help and support. Apply for scholarships, and get grants for your school.
Math TV Problem Solving Videos is an innovation learning project for middle school students. According to Noreen McGrath (email communication July 27, 2004), the grade 6 math teacher who recommended this site, "The goal of the project is to get middle school students excited about problem solving in mathematics. Students send in word problems which, if selected, are incorporated into a video which shows a very detailed, step-by-step explanation of how to solve the problem. The narrator of the fictional Math TV show, Infinity Quick, emphasizes a logical approach to problem solving and utilizes a variety of strategies. At the end of the video students are invited to try a similar, interactive word problem complete with helpful hints and tools." Math TV indicates that the practice area has an online calculator and notepad for testing ideas and making a drawing. Whole numbers, fractions, percentages, ratios, probability, algebra and geometry are among topics explored.
National Math Trail: This project receives support from the US Department of Education's Star Schools program, through the Satellite Education Resources Consortium (SERC), and NEC Foundation. K-12 teachers and students share the math that exists in their own environments. "Students explore their communities and create one or more math problems that relate to what they find. Teachers submit the problems to the National Math Trail site, along with photos, drawings, sound recordings, videos--whatever can be adapted to the Internet." Submissions are posted to the site, and indexed according to grade level and math topic. The site clearly addresses NCTM standards, including connections, communication, problem solving.
Project Exchange is a place for teachers to share project-based high school curriculum: visual and performing arts, mathematics, science, language arts, social studies, digital design, and world language.
Statistics: A Curiosity Factor is a project suitable for use with middle school or high school students studying the concept of collecting and analyzing data. It also provides an introduction to survey research.
Teach 21 Project Based Learning from the West Virginia Department of Education contains projects in several content areas: mathematics, reading/English language arts, science, social studies, and so on. Pick your subject and grade level. Mathematics, for example, includes projects for grades 3-8 and high school, including for algebra 1, geometry, algebra 2, conceptual mathematics, probability and statistics, trigonometry, pre-calculus, and calculus.
Teacher Tap: WebQuests. If you are not confident about designing your own WebQuest, this resource will help you to locate and evaluate WebQuests by grade level and content area that have been designed by others.
ThinkQuest The Library contains over 7,000 projects build by kids for kids. Math subcategories include geometry, chaos theory, fractals, algebra, trigonometry, statistics, probability, calculus, arithmetic, and puzzles. You can also create projects for classes, or join existing projects and collaborate with others.
Wonders of Math from the Galileo Educational Network Association and Mt. Royal College in Calgary, Alberta, Canada contains a number of inquiry based activities with special sections devoted to "That's a Good Problem," puzzles with printable worksheets, elementary and secondary project investigations, Japanese Lesson Study, and additional resources.
Do you need 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 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, including videos. A handbook is 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.
Want to create a telecollaborative project from scratch?
NickNacks Telecollaborate: Site contains links to numerous collaborative projects and how-to information.
What is a real WebQuest?
Consider 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:
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.
If 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:
RubiStar provides 10 steps to creating a rubric. If you don't have time to create your own, use the customizable templates from nine categories. Math templates are provided for graphing and problem solving. After your students have done the project and the rubric has been used to grade it, you can use RubiStar to analyze the data to determine which items are problematic for the class as a whole.
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.
David Warlick of Landmarks for Schools (http://landmark-project.com/) reminds teachers and students to seek permission when using information from web sites designed by others. He has provided simple to use Permission Templates for this purpose, which will automatically go to the author or web master of the site you wish to use in instruction or for a school project. Use his Citation Machine to automatically create references in APA, MLA, Turabian, or Chicago format. Students then can cut and paste those references into their projects.
Share Classroom Projects with an Authentic Audience.
Students can create a web site within minutes using Jottit.com--really they can! Use it for sharing classroom projects with not just the teacher, but with family, friends, and the community. The site can be set up for private or public viewing, and can be customized. You can also set the level on who can edit the content. Of course, there are other services that students can use to post content to the web.
Consider having your students create their own digital storybooks to display projects. Mixbook is free and can be used as a collaborative classroom tool for that. There is a program for educators, too, to create student accounts for better management.
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
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/
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/
Learn about the technical side of creating multimedia projects, including working with images and video.
See CT4ME Technology Integration