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Project Based Learning Examples (six of them)

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Project Based Learning Examples (six of them)

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by Janet Pinto, Chief Academic Officer at Curriki

I wish geometry was taught in this way when I was in school.

Curriki's new Project-based Learning (PBL) high school Geometry course is now available. For so many students, it's difficult to make a real-life connection between math and their everyday lives. By adopting a Project-Based Learning (PBL) approach, students learn that geometry is not only theoretical, but practical and necessary. Students will move beyond a basic understanding of concepts to an enjoyment of discovery.

This free Geometry course not only leverages the popular PBL "active" approach but is also aligned to Common Core State Standards. Thom Markham, Ph.D., President of PBL International, is the designer of the course. He notes that Project-Based Learning points us toward the future of education. "It's a proven method for integrating the 21st century skills of communication and teamwork into the delivery of core subjects."

Available online at the Curriki site, Curriki Geometry is designed to meet the needs of students raised in a global, interactive, digitally-connected world through the use of real-world examples, engaging projects, interactive technologies, videos and targeted feedback. Developed with funding from AT&T, the Curriki Geometry course is modular, so can be used as the foundation for students' Geometry 1 curriculum, as a supplementary resource, in an after-school program, or in a homeschool environment.

The course units have been designed with carefully selected Curriki instructional materials, interactive content, videos and other materials that students can explore and use as they solve the series of challenges in each unit. The course structure is based on the six Common Core High School Geometry topics, organized in six projects:
Project-Based Learning in Math: 6 Examples
1. Selling Geometry

This project introduces students to a brief history of geometry, geometric terms, geometric shapes, and transformation and manipulation of shapes through reflections, tessellations, and dilations. Students will form marketing teams to "sell" geometry by explaining key terms, demonstrating key shapes, and describing the significance of geometry to an audience

2. Designing a Winner

This project allows students to apply the geometric principles of triangles, volume, and coordinates to the mapping and design of a multi-purpose arena in a limited area. The arena must serve as a venue that can be easily converted for use by two sports, plus serve as a concert venue if needed. Students will form design teams to create a map showing how the arena can be converted for the two sports. The map will be accompanied by a hand-built model or a digital design using Google SketchUp or other tool. In the final presentations, the map and design ideas will be presented to the local City Council.

3. What's Your Angle, Pythagoras?

One real-world task students must learn is the ability to explain what you know to others. The challenge in this project is for older students to find common examples of right-angle geometry and use their geometric knowledge to create a lesson that explains Pythagorean principles to younger students in a way that is engaging, understandable, meaningful, and relevant.

4. TED Talk: House of the Future

The challenge in this project is for students to examine trends in housing, extrapolate that information to predict the future, and use their geometric modeling skills to design a house that supports their predictions. Students will create a floor plan and basic model of a house of the future that reflects four trends and then deliver their design and give evidence of their thinking in the form of a 10 minute presentation about why their house will be necessary and useful in the future. The format for the talk can vary, but it is suggested that the presentation follow the guidelines for a TED-like talk in which presenters give short presentations that focus on the future and innovation

5. The Art of Triangles

This project teaches students the basics of triangles, such as types, congruence, proofs, and similarity, by asking each student to create a poster, drawing, or personal adornment such as a fingernail design, piece of jewelry, or tattoo that uses at least two different triangular shapes. The product must meet the criteria for 'beautiful'-that is, it must display symmetry or other design elements that make it attractive.

6. How Random is My Life?

This project is designed to have students work through and master basic problems in probability, and then apply that knowledge to authentic issues in which statistics and probability play large roles. The topics should apply to teen interests and concerns. Students will be given the opportunity to research and choose their topic. However, topics may also be assigned by the teacher in one of four areas:

1. Driving and cell phone use
2. Diet and health
3. Professional athletics
4. Costs associated with a college education

After researching the issue, students are expected to explain how probability affects their lives in each of these areas, and to make recommendations to other teens on actions that can improve their chances of making good decisions on each issue

The Common Core Math Practice Standards are woven through each unit, with projects and explorations designed to develop students' mathematical "habits of mind", problem-solving and reasoning skills, and abilities to use mathematical models and technology tools strategically.
Project-Based Learning in Math: 6 Examples; image attribution flickr user vancouverfilmschool

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Project-Based Learning in Math: 6 Examples

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by Janet Pinto, Chief Academic Officer at Curriki I wish geometry was taught in this way when I was in school. Curriki's new Project-based Learning (PBL) high school Geometry course is now available. For so many students, it's difficult to make a real-life connection between math and their everyday lives.

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Overview of how to use Constructivism in a Math Class

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Overview of how to use Constructivism in a Math Class

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Problem based learning for math (OVERVIEW

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Problem based learning for math (OVERVIEW

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A deep dive on using problem-based tasks in math

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Math Project-based Learning is a companion IAE-pedia document that covers Project-based learning (PBL) in math education. As the Venn diagram given below indicates, Problem-based Learning and Project-based Learning overlap. Since they are both abbreviated PBL, and they overlap, it is easy to confuse the two.

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Another Overview of Contructivism in a Math Class

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Another Overview of Contructivism in a Math Class

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Math Forum - Constructivism in Mathematics Education

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Internet resources that address constructivism in the math classroom, one of the Math Forum's series of pages dealing with issues in math education.

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Inquiry Based Learning Example (With Video)

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Inquiry Based Learning Example (With Video)

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Mary Ellen Tyrell and Sapphira Hendrix do not teach at the same schools. They do not know each other. They do not even teach the same grade levels. However, they are both extraordinary math teachers who are totally committed to using ISA's inquiry-based approach to teach math. Tyrell is the STEM Department Team Leader at the Institute for Health Professions at Cambria Heights, and Hendrix teaches ninth grade Algebra at Brooklyn Preparatory High School. What these two teachers do have in common is a strong relationship with their ISA coaches that has facilitated their development and implementation of inquiry in their math classrooms.

"When I started teaching," Hendrix said, "I had an idea of the kind of teacher I would be. I thought that I would teach the way that I was taught. I would lecture and model how to work a problem. Students would take notes, solve practice problems quietly at their desks, do homework, and love math like I did. I was totally unprepared for 30 ninth graders who were not naturally in love with math. I don't know how I would have survived my first year without the consistent help and support of my ISA coach." Tyrell agrees. She primarily used the I do; we do; you do pedagogical strategy during her pre-ISA coaching years. "Now," she says," my classrooms are 100% student-centered, not teacher-centered. The students take ownership of their learning. My students predict, make inferences, pose ideas and defend them, and have discussions with their peers about why they used a certain process to solve a problem. Their voices, thoughts, and ideas are valued and respected. Using the inquiry approach to teaching math is the best preparation that they could possibly get to succeed at the college level."

Tyrell says, for example, that prior to support from her ISA coach she taught quadratic equations in a more teacher-centered way. Now she presents her students with tasks such as: How long after you take a time-released medication will you have to wait to take another dose? Such tasks require students to represent their solution graphically and as an algebraic equation as well as orally share their thinking with the class. The inquiry approach requires students to integrate knowledge, skills, and concepts and apply a body of knowledge to solve a real-life problem. "They have to demonstrate deep understanding of math, and they have to think critically to perform well on these kinds of tasks," Tyrell states. Hendrix points out that math skills, procedures, and processes are embedded in the tasks. "Using inquiry really promotes procedural fluency because the math procedures and skills make sense to the students," she states.
See an inquiry-based math lesson by clicking here.
Both teachers attribute their development of inquiry pedagogy to their partnership with their ISA coaches. "I can't imagine being able to meet the demands of Common Core without having had the excellent coaching that I received through ISA," stresses Hendrix. She explains that it was the consistent weekly feedback based on observations in her own classroom and subsequent forward planning that helped her shift her instructional practice. "My coach and I went over every lesson before I presented it to students. One of the biggest benefits of this process was discovering my own knowledge gaps and working with the coach to close them before I tried to teach the students. "Having access to the ISA curriculum was also a huge benefit Hendrix recalls. "It took me eight hours to design a 50-minute lesson. There is no way that I could have designed a lesson from scratch every day."

Tyrell says that the benefits for students of using the inquiry method are not just confined to math. She is proud of how confident and courageous her students have become. "They are not afraid to try even if they do not know exactly how to do something." Tyrell states that she gives each student an ISA performance task so they can demonstrate what they have learned. "I always include one element of something that is unknown, and they are never stymied by this. Not one student pushes the paper away and says, 'I don't know how to do that.' The question that I constantly ask myself is: What do I want my students to do with their lives? I want them to be prepared to be CEOs, not cashiers. I expect them to function at the highest levels possible so that they have real options in life. Using the inquiry-based approach to teaching and learning fosters attitudes and beliefs that will serve them well over their lifetimes. There is nothing in the world I would rather do than this."

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The Inquiry-based Approach to Teaching Math: Teaching Students to be Mathematical Thinkers - Institute for Student Achievement

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Mary Ellen Tyrell and Sapphira Hendrix do not teach at the same schools. They do not know each other. They do not even teach the same grade levels. However, they are both extraordinary math teachers who are totally committed to using ISA's inquiry-based approach to teach math.

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This is a jigsaw collaborative learning activity on the topic of Systems of Equations

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Service Learning Overview (with Video Ideas)

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Service Learning Overview (with Video Ideas)

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Service Learning Projects to Engage Math Students

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Service learning is different from volunteerism. Volunteerism is defined as the use of volunteer labor to do work that needs to be done. Service learning is like volunteerism in that work that needs to be done is done but in addition, there is an important academic component in the work.

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Math teachers: This is for you. Here are some great suggestions from efriend and math afficionado, Matt Kim:

***

Before I was ever a high school math teacher, I was always a hardcore technophile. As long as I can remember, technology has been one of those things that have caught my interest no matter what my current job title was at that time. It makes sense that when Jacqui and I were talking about popular tech tools and ways to bring tech into the k-12 math class, I had a lot to share and get excited about and jumped at the opportunity to write this post. It really is an exciting time for technology in education and the tools available to us to use today in our math classes is no exception. Just a disclaimer though, I am a high school math teacher, so a few of the tech-tools I reference in this post belong mostly in a secondary math classroom, but with a little elbow grease and ingenuity, there are ways to fit them into any K-12 math curriculum as well. For the most part, these are just great ways to incorporate tech in your math classroom so feel free to give them a try!

1. If you're a math teacher and have never heard of Desmos, you've been either living under a rock or need to upgrade your math-teacher game pronto. While TI calculators are still ubiquitous and useful especially when working in higher math classes like Trigonometry or Calculus, Desmos is an online graphic calculator that can do everything the $100+ TI calculators can do and more (and did I mention it's free?). If you are teaching in a 1-to-1 device classroom, the Desmos team has done an exceptional job in bringing math education into the 21st century. Desmos has created an activity builder that teachers can use to build interactive lessons that students can do on their own tablet or Chromebook devices while the teacher monitors student work in real time. What's more, they have curated the best lessons into a comprehensive library of lessons that are free for teachers to use as well! Check out teacher.desmos.com to create your own activities or use some of the featured lessons already there.

2. Geogebra is very similar to Desmos in that it harnesses the computing power of classroom devices (tablets or Chromebooks) to do things that required a $100 device to do before. In a nutshell, Geogebra is a program that you can run in a web browser or a standalone app that can you can use to demonstrate math concepts in graphical representations. I have to be honest, it can be a little too technical to use for the average user, (or at least it was for me). The interface isn't as intuitive as the Desmos activity builder, but the good news is that they have a library of 400k+ lessons that you can search from and so I didn't really have much of a problem finding a lesson someone else had programmed and found a way to fit it into my lesson. Even if you don't have a 1-to-1 device classroom, there are a lot of great examples in the Geogebra library that you can project in front of your class to demonstrate an otherwise abstract mathematical concept and have a great class discussion about what they are observing.

3. On the surface, the idea behind Nearpod isn't very groundbreaking or unique in any sense. Nearpod is described as a mobile app that allows teachers to create and share interactive multimedia presentations in 1-to-1 device classrooms. I once heard a colleague describe it to me as a very fancy PowerPoint presentation, but in my opinion, that is an overly simplistic description of it. Yes, the lessons are built around a presentation platform, but Nearpod does a good job of incorporating interactive elements like polls, question and response, the ability to draw on screen, and so much more. What's more, they have a fantastic library of lessons created by teachers who use Nearpod in their own classrooms. If you're a particularly enterprising teacher, they are currently accepting applications to become a Nearpod author where you can create and sell lessons on the Nearpod platform to earn some supplementary income. Although this list is specifically being written for a math classroom, the nice thing about Nearpod is that they have a library of lessons that covers other subjects as well like ELA, Science, Social Studies, and even Digital Citizenship.

4. Let me start off by saying that of all the recommendations on this list, I am fairly confident that Kahoot will easily be the most popular learning tool you use with your students. Why? Well, because Kahoot is a powerful educational tool (backed by a lot of good research) in the guise of a VERY addicting game format that you can play as an entire class. The basic premise behind Kahoot is fairly simple: Teachers create a series of multiple choice questions that are projected on the screen while the students answer those questions on their own devices. The game element comes into play because after every question, the top ranking participants are displayed before moving onto the next question which really ramps up the competitive spirit in almost every classroom I have seen use Kahoot. One of the really great things about Kahoot is that it is extremely easy to set up and students do not need to create an account to participate. All they have to do is navigate to the Kahoot website, input the code for the quiz that the teacher provides, and they're off to the races. As a high school math teacher, I have used Kahoot in my classes more times than I can count, but so has my wife who is a first grade teacher, and it works just as well there as well!

5. As its name suggests, Formative is an online tool that teachers can use to create formative assessments (you see what they did there?) and make it super easy for teachers to instantly gather student data on any given subject. The real power behind Formative is in its ability to convert any PDF or Word document into an interactive assignment that you can give to your students, have them do it on their devices, monitor their progress in real time, and give feedback to them instantly. This really cuts down on the feedback loop for students because instead of waiting a few days for the assignment to come back to them corrected (if at all), the teacher can give feedback almost instantaneously as the assignments are turned in. If you're like me and have entire file cabinets of old worksheets in PDF or Word formats, Formative is a great way to breathe a second life into those worksheets and turn them into interactive lessons that you can assign to students.

6. Google Apps For Education (GAFE) is another one of those tools that you are either using currently, or eventually will use in the near future thanks to the ubiquitous nature of all things Google. I have worked in 3 different school districts in my career as a teacher and GAFE has been rolled out in all 3 of those districts at some point in my time at each of those districts. To be quite honest, it's really easy to overlook the usefulness of GAFE as there's nothing ground breaking about most of the apps provided in the suite. You have Google Slides which is an online presentation tool in the vein of PowerPoint, Google Documents which is essentially an online word processor, and also Google Sheets is an online spreadsheet app very much like Microsoft Excel. However, GAFE also provides apps like Google Classroom which allow you to organize your students into classes, assign assignments, create assessments using Google Forms, etc. In fact, there is so much functionality built into GAFE that they offer certifications to become a Google Certified Educator, and even have entire conferences called GAFE Summits that teachers can attend to receive training on the latest developments in the world of GAFE. What's more, some rockstar teachers like Alice Keeler have entire websites built around GAFE explaining the functionality usefulness of those apps in the classroom.

The next four recommendations are not necessarily tools to use with your students, but they are tech tools that will definitely enhance your teaching practice in a way that just wasn't possible until fairly recently.

1. Twitter is probably one of the most misunderstood tech tools available to teachers today. It's misunderstood because its widely hailed as a social media tool, but no one bothers to explain why and how to use Twitter effectively as a teacher. I won't bother to explain it in too much detail because I wrote a much longer piece on my thoughts about why teachers should twitter, but I will say that Twitter is probably the single most powerful way for teachers to network and communicate with other educators around the world in real time to share thoughts, lesson ideas, and inspiration to improve their own practice as a teacher. Also, since this is a list specifically for math teachers, there is a special Twitter hashtag, #MTBoS, which is an acronym for Math Twitter Blog oS phere which has grown to become one of the largest and most vibrant Twitter communities with literally thousands of math teachers contributing, and having discussions about their math classes on a daily basis. This really is an invaluable resource for math teachers if you know how to use it.

2. CoffeeEDU is an idea started by Alice Keeler (who makes her second appearance already on this list) and the basic idea behind this is to organize educators to meet in a physical location to hold an "un-conference" which means that the meeting should be an impromptu, unscripted, conversation style meeting that is as unrelated to a presentation style professional development as possible. There are a whole bunch of guidelines that Alice has taken the time to put together so please go check them out at the link posted above. While this isn't necessarily a tech tool, I will say that I have been to two CoffeeEDUs in my area and at both meetings, people made recommendations about tech tools and websites that I had never heard of. Oh, and it was just plain fun actually meeting and network with some educators in my area that I would not have had the opportunity to meet if it weren't for gatherings like this.

3. Start your own blog

If you don't have your own blog already, you should start your own teaching blog as soon as possible. Without exaggeration, blogging has transformed my teaching practice more than any single tool or resource listed on this post. Blogging allows you to metacognitively reflect on your lessons, write about what went right and what went wrong on any given lesson, share ideas with other teachers, and just provide yourself with a place to record your thoughts. One of my favorite things to do is look back on my past blog posts and see how far I've come as a teacher. It is both humbling and enlightening at the same time and easily the most important tech tool I have in my teacher's bag of tricks.

4. Read and follow other teacher's blogs

Every single one of the tools I have mentioned above have come from my reading other math teacher's blogs and digging through the veritable treasure troves of information that they shared with the Internet for free. Here're just a few of the teachers I follow and recommend for you to follow as well (in no particular order):

These are just a few of the teachers that started me on the path towards blogging and there are many more that I wanted to put on this list, but this is a good place to start. You should start your own list of teacher/bloggers to follow and contribute to the growing community of math teachers on the internet as well!

"Matthew is a husband, father of two, a lover of all things pizza, and a high school math teacher (not necessarily in that order). He's a big believer in incorporating as much tech in his lessons as possible and preparing his students to be 21st-century learners. You can find him at Tips4Teachers.net where he blogs about education and his personal blog, Mathmattics.com."
More tech resources about math
Math bundle of lesson plans

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Math teachers: This is for you. Here are some great suggestions from efriend and math afficionado, Matt Kim: *** Before I was ever a high school math teacher, I was always a hardcore technophile. As long as I can remember, technology has been one of those things that have caught my interest no matter what my current job title was at that time.

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By Patty Reed

In Common Core Math I have seen my students struggle many times through story problems in class and on testing. I realized that most of my students were having a difficult time understanding what they are being asked. The "mathematics genre" with word organization, choice, higher level of thinking, and above level content was throwing them off and confusing at best. Knowing that students must be able to answer to a higher level of depth of knowledge questions, understanding these questions are a problem for students reading at or below grade level, ELL's, and special needs students.
Why do we need to teach math literacy?
"Mathematics is particularly difficult content to read, presenting demands in higher-level thinking and comprehension skills. Many students may not easily comprehend mathematics texts, even when they are able to decode print materials (Cantrell, Burns, and Callaway 2009). Mathematics texts make heavy use of precise symbols and unfamiliar vocabulary; use longer and more complex sentence structure; contain more words, symbols, and concepts per paragraph than other texts; and have little redundancy to help with interpretation (Schell 1982). Further, mathematics texts are often written above the grade level of intended students (Barton and Heidema 2002; Reehm and Long 1996). Concepts critical for understanding may be hidden, implied, or left unstated. In reading mathematics text, readers need to analyze and expand meaning rather than condense ideas (Fuentes 1998; Shanahan and Shanahan 2008)."

1. Students need to learn comprehension of mathematical language and how it relates to operations.

2. Mathematics uses different sentence structure than English Language Arts.

3. Math doesn't have a one to one correspondence with math symbols and words.

4. Math uses highly technical vocabulary, symbols, and multiple meaning words.

5. Distractors or unnecessary information is included in math questions.

What is Reciprocal Teaching?
Looking for a way to help my students better understand, I came across Reciprocal Teaching through my literacy teammate. (It is also listed #11 on Hattie's list of student achievement indicators.)
What Reciprocal teaching can do for students?
Reciprocal teaching is an interactive strategy and a collaborative learning method. This strategy is used mainly for literacy development to promote reading comprehension skills. But it can be adapted to students' comprehension of mathematical word problems.
5 parts of Reciprocal Teaching in Mathematics 1.Questioning is used to identify key parts of the problem.

1. It helps students understand the meaning of phrases, symbols, and vocabulary.

2. It provides structure for problem solving.

3. It helps students identify important and unimportant information in a question.

4. It teaches students critical thinking in predicting, clarifying, questioning, and summarizing is essential in all content areas.

5. Encourages students to talk about the math and how they solved a problem.

6. Helps students see multiple ways to solve a problem.

What do we notice?

What do we wonder?

What is this problem asking us to do?

What should we do first, second...?

Does anyone have questions about this problem?

Are there any words, phrases, or symbols we are unfamiliar with?

What information is needed to solve this problem?

What are the facts we know?

What information can we eliminate?

3.Predicting
I see this step as so important. There are usually just one or two words in a problem that will through off a student. This can totally turn around the intended meaning of a problem, cause confusion and misunderstandings for students.
How to implement reciprocal teaching in your classroom?

What type of mathematical questions are we being asked?

What mathematical operations may be required to use?

What do we think this problem is about?

What do we estimate the answer to be?

Devise a Plan to solve the problem.

What are your strategies/plan to solve this problem?

Can we use pictures, diagrams, numbers or words to solve this problem?

Have we had a problem like this before?

Summarize the purpose of the problem.

Did we draw a diagram or a picture to solve this problem?

How do we justify our answer?

What did it ask us and how did we solve it? Give evidence for your thinking.

How did we check this problem?

How would we approach this problem if we were presented with a similar one?

Were there any misconceptions about this problem?

Results of Reciprocal teaching in my classroom

Use role cards for each student that gives sentence stems and steps.

Explicitly teach the stages whole group with a problem, and then have groups model the process while the rest of the class watches, notices, and comments.

Guide students through each step in small groups.

Gradually release responsibility to students.

Bookmarks can be given with roles for quick reference after students have the process down.

Math Reciprocal Teaching Resources: RECIPROCAL TEACHING IN MATHEMATICS Making meaning in mathematics problem-solving using the Reciprocal Teaching approach

Lower math anxiety for students

Students have more confidence in solving a problem.

Students work together at higher levels.

Students are gaining abilities to complete complex tasks.

It is providing support and a framework for ELL's, special needs students and struggling readers.

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By Patty Reed In Common Core Math I have seen my students struggle many times through story problems in class and on testing. I realized that most of my students were having a difficult time understanding what they are being asked.

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Remember, this type of lesson should be about a topic that the students can pick legitimate sides on and there is evidence for both sides. (can be hard for math)

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On Thursday evening Leslie and Brian spoke at Boston College as part of the ATMIM (Association of Teachers of Mathematics in Massachusetts) Winter Conference. Our presentation was on making mathematics meaningful to students. We shared, did and discussed math activities from our site with our participants. We also mentioned other web resources that provide free math activities that are meaningful to students and wish to mention them here as well.

1. Dan Meyer: http://blog.mrmeyer.com/ Patient Problem Solving and hooking students into learning math through the use of video. On the right-hand column of his blog, Dan has a section called "My Curricula" which contains some wonderful activities. Dan's philosophy is presented in this TED presentation.

2. Emergent Math: http://emergentmath.wordpress.com/ Inquiry based activities.

The following are some sites where we find tons of useful data that you can use in your own creations.

Do you have a site that you would like to suggest that has free authentic math problems or activities? Or do you have a site that offers loads of good stats? If so, please leave your suggestion in the comments of this post! 🙂

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Free Resources for Authentic Mathematics

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On Thursday evening Leslie and Brian spoke at Boston College as part of the ATMIM (Association of Teachers of Mathematics in Massachusetts) Winter Conference. Our presentation was on making mathematics meaningful to students. We shared, did and discussed math activities from our site with our participants.