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Instead of doing math problems with no context, students at this school role-play real jobs.

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That hit me like a rolled-up newspaper.

As I absorbed this veteran educator's words, I realized that not only was I wrong in my assumption that I (or any teacher) is a meanigful audience, but also that my assumptions about how grading and assessment work were so far removed from modern research that I might as well have been a 21st-century doctor treating humours.

Over the years I've come to believe that the use of single-shot, for-point assessments is one the worst possible things we can do to students. If the students don't recognize assessments as a chance to show their learning, then these things aren't even assessments; they're something altogether alien to real learning.

Fortunately, there are many approaches we can take within our own classrooms to change this situation. With a few changes, we can make assessment a loved part of the educational process.

Here are a few ideas to get started.

Change Your Gradebook into a Logbook

Only list things in your gradebook that students and parents can Google. If the search of that assignment title doesn't bring up the beginning of the breadcrumb trail you intended, then you need to word it better.

I used to list things like "Quiz 1" or "Homework from Chapter 3" in my gradebook. No one has any idea what those are, and if those scores are low, no one has any idea how the kid can improve them.

This is opposite of how psychology shows that humans work. We want to be shown our mistakes so we can fix them. Student grades need to fluidly move up and down as kids show learning, retention or lack thereof.

So, start listing the big ideas from your course as your assignments. A parent can really help their kid when they know they've got these grades:

1. Net Force and Vectors: 5/10

2. Momentum: 9/10

3. Energy Conservation: 10/10

Finally, allow those numbers to change as you learn more about the student's abilities -- or, in keeping with the intention of school, as he or she learns more throughout the year!

My students have noted this in every end-of-course evaluation I've given them: the fact that they can change their grade by mastering the material is so much more enabling than bringing in a box of Kleenex for ten arbitrary points.

Allow for Alternative Assessment Types

This is the key to a reformed performance assessment strategy. Since the '70s, we've known that people of equal ability assess differently depending on the assessment schema. ¹

This matters. A lot.

If a student is capable but assessing poorly, that student will only persist for so long until he or she quits, and that's the stuff of tragedy.

Here are some things I've used as formative and summative assessments:

1. Paper Quizzes

I can hear you groaning, but they still have a place as long as the students see them as plastic instead of concrete -- a tool of many uses instead of a make-it-or-break-it moment. Students also need to see quizzes as an opportunity to let you, their teacher, into what they don't know. Ask questions that demand meta-cognition. Have them identify the limits of their abilities. Quizzes need to inform a larger picture painted in tandem with some other assessment options.

2. Product-Oriented Projects

Build this, fix that. I have students hanging Calder-style mobiles from my ceiling right now to assess their understanding of torque.

3. Process-Oriented Projects

Product is irrelevant; the flowers-stopped-and-smelled are all that matter. This is often how things work in math courses. We want students to learn the parlance and joy of curiosity simply by trying to answer a question. I recently had students fail at colliding two rockets, but they admitted to knowing more about calculus, rockets and trajectories than they ever would have learned by staying in the classroom.

4. Interviews

Pull students from the hallway during lunch or before school, and have a heart-to-heart about a learning target they don't get. Find out what they really don't know. Ask them to verbalize the big idea. Ask them to explain what part they always get stuck on. Ask them if they have context. Why would you want to know how to find the directrix of a parabola? Do one or two of these interviews each day, and just keep cycling through your students.

5. Writing

Ask essay questions in math. Ask for big ideas. What are the limits of calculus? What would math be like if the library at Alexandria hadn't been sacked?

6. Art

Can the students demonstrate the concept beautifully? Provocatively? Can they force a conversation about their learning just by creating something? I once had a student create a mirror etched with images of corn kernels. I've never had such conversations about corn's prevalence in the American diet. That was a biology class to remember!

7. Ditch the Numbers

You don't have to use points to grade students at all. Keep a running journal online of the work they're doing on each of your learning targets. Add your own feedback into the conversation, and upload the work that the students do to prove they're proficient. These records will be thousands of times more valuable than any GPA when they apply for jobs and college admission.

The key here is that the assessment of the student hinges on combining data from more than one of these options. Take a student's performance on a quiz about ancient Egypt. Combine that with an oral interview later in the year about Egypt's influence on Rome. Finally, combine those two data points with a mapping project showing the flow of trading through the ancient world. Now you can decide how much that student knows about Egypt. If the quiz doesn't match, perhaps it's OK to throw it out.

Announce Learning When You See It

In physics this week, a student puzzled so deftly through a laboratory setup to study collisions that I was powerless against his knowledge. He refused my instructions to set up an impossible pool shot, and formed the physics into a palpable argument, not because I was testing him, but because we were having a conversation. I immediately gave him full credit for our learning target about momentum, because there was no way that he didn't understand the big idea.

Later I'll see how he performs on a pencil-paper test, but for now, I'll record what I know about him.

This flexibility in reporting has a manic effect on the other students. They can't wait to show off how much they know. They also can't wait to talk about what learning looks like. Win.

Seek Out Authentic Audiences

All of this is moot if the students aren't blazing ahead, motivated by the ingrained social need that comes with being human.

Most teachers' first foray into this approach often involves having an expert of some sort (mine was an engineer at a local firm) come in to critique a student's project. This is cute, and often has some positive outcomes, but it's a billion times more powerful to have the student select the audience out of necessity.

Ensure that it is impossible for the teacher to be the audience. That's what it means to have found authentic audience in your classroom.

I once watched a room full of chemistry students furiously fermenting an exotic species of switchgrass. The fervor in the room was contagious, and I jumped in to help.

I asked the students why they were so excited, and one turned to me and said, "This is for a town in the Philippines. We Skyped with them last week, and we found some of the same grass they have. We want to help them make ethanol. Regular gasoline is a really high cost of farming for them, and they have a lot of switchgrass."

I almost tripped over what seemed too contrived to be true, but I realized that these kids were actually doing what people claim to want to do: they found a problem, and they were fixing it.

Finding authentic audiences can be complicated and often time-consuming. Get on Monster.com, find the companies in your area that do what you teach, and email the secretaries. Find the local college professors that teach what you teach and ask them to explain their research to your students. Start curating a list of community members that will donate time and resources to your school, and don't be afraid to email all of them whenever you need ideas or materials.

Most importantly, find someone who has a question to which no one knows the answer. Trust the content of your core curriculum to show its face while your kids investigate Chaucer, or wind energy, or programming, or whatever.

I asked the teacher of the switchgrass students how she knew if her students were learning any chemistry. She laughed at me.

Sources

¹ Marzano, Robert. http://www.marzanoresearch.com/research/about

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Deeper Learning: Performance Assessment and Authentic Audience

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That hit me like a rolled-up newspaper. As I absorbed this veteran educator's words, I realized that not only was I wrong in my assumption that I (or any teacher) is a meanigful audience, but also that my assumptions about how grading and assessment work were so far removed from modern research that I might as well have been a 21st-century doctor treating humours.

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While many teachers recognize the value of inquiry-based learning, most find it a difficult approach to teaching mathematics. The traditional way of teaching math by figuring equations and plugging in numbers focuses only on computation. Teachers have taught math this way for years, and it has developed such a poor reputation that students may actively dislike the subject or find it intimidating. New ideas and perspectives on teaching math may help overcome this challenge.

In inquiry-based learning, teachers use questions, problems and scenarios to help students learn through individual thought and investigation. Instead of simply presenting facts, the teacher encourages students to talk about a problem and draw on their intuition to understand it. Inquiry-based learning also focuses on letting students ask their own questions - essentially providing their own inquiry. Student-led questions follow teacher-guided inquiry.

Instead of lecturing about learning goals, the teacher cultivates a learning environment and helps students explore it through questions and experiences.

1. Process focus
When students solve problems themselves, they internalize conceptual processes. Inquiry-based teaching prioritizes process over product.

2. Investigation
The teacher may pose a problem derived from the class content or students' questions. The students then investigate the issue to find an answer.

3. Group learning
Students may work in pairs or in small groups when exploring a problem. Students assist one another throughout the learning process, which enables them to share and build upon ideas as well as articulate how they arrived at a solution.

4. Discussion monitoring
As the students work together, the teacher can move from group to group, listening to their discussions. Teachers may ask questions to gauge students' understanding and correct any misconceptions.

5. Real-life application
Students solve math problems that have a meaningful life application. For example, a teacher may present a multiplication problem as an interesting story: "Brittany has 2 bags of candy. Each bag has 4 candies inside. How many candies does Brittany have altogether?"

Teachers may wish to focus less on math computation and more on helping students determine which pieces of information are useful and how this information applies to the real world. Teachers can develop students' understanding of the topic with guided inquiries.

Think about what you want your students to know or do before class.

Start with one or more overall guiding questions.

Inform students that there are multiple ways to solve a problem.

Model how students can develop their own questions.

Teaching students to ask higher-level questions is an important aspect of inquiry-based learning, but what kinds of questions work? Three ways that a teacher can successfully model questions to students include the following:

1. Ask big questions that have more than one answer.

2. Think about how to model questioning across a range of grade levels.

3. Phrase your questions in a way that fosters individual exploration.

The following example illustrates the use of an inquiry-based math strategy in the classroom:

An inquiry-based classroom discussion helps learners understand the concept of slope. The teacher draws a picture of two hills: one taller and one longer. The teacher asks, "Which hill is steeper?" The question may stimulate a lively discussion or a debate about the correct answer.

Inquiry-based learning involves guiding students by asking more in-depth questions - questions that encourage students to pose high-level questions themselves. This type of teacher-guided inquiry can motivate students to think critically and to appreciate learning.
Learn about the University of Texas at Arlington M.Ed. in Curriculum and Instruction - Math Education online program.
Sources:
Edutopia: Inquiry-Based Learning: From Teacher-Guided to Student-Driven Strategies for Teaching Elementary Mathematics: Inquiry Teaching: Models of Instruction KQED: How Can We Teach Math to Encourage 'Patient Problem Solving'? Have a question or concern about this article? Please contact us.

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How Inquiry-Based Learning Can Work in a Math Classroom

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While many teachers recognize the value of inquiry-based learning, most find it a difficult approach to teaching mathematics. The traditional way of teaching math by figuring equations and plugging in numbers focuses only on computation. Teachers have taught math this way for years, and it has developed such a poor reputation that students may actively dislike the subject or find it intimidating.

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Edutopia is a free source of information, inspiration, and practical strategies for learning and teaching in preK-12 education. We are published by the George Lucas Educational Foundation, a nonprofit, nonpartisan organization.

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Math class needs a makeover -  Dan Meyer

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I met Greg Schwanbeck at Apple Distinguished Educator sleepaway camp last month. He teaches science. I teach math. We set those differences aside and found a connection. I use multimedia in my curriculum. Greg uses video for assessment in a way I found compelling.

Let's say he wants to assess the impulse-momentum theorem, which is the theorem that explains why boxers roll with punches rather than against them. ie. If you double the duration of the impact, you halve its force. (Cut me some slack here, science-buds. Everybody knows I have no idea what I'm talking about.)

He gave me permission to share with you three versions of the same assessment of a student's understanding of the impulse-momentum theorem. Let me invite you to assess the assessments in the comments. List some advantages and disadvantages. Ask yourself, "What is each option really assessing?" Greg will be along shortly to offer his own commentary and to assess your assessment of the assessments.

An 80 kg stuntman jumps off of a platform high in the air and lands on an airbag. The stuntman hits the airbag with an initial velocity of 45 m/s downward. 0.1 s elapses between the moment the stuntman first touches the airbag and the moment the airbag completely deflates and he comes to rest. Assume that the maximum force that the stuntman can experience and survive is 39200 N. Does the stuntman survive the fall?

A stuntman jumps off of the top of a crane extended high up in the air. Below him is an airbag-a large inflatable cushion that has a thickness of 3 meters. When the stuntman comes into contact with the airbag, the impact deflates the airbag over a period of time, compressing the airbag from 3 meters thick to 0 meters thick while slowing him down to a stop. Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive.

Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive the jump.

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I met Greg Schwanbeck at Apple Distinguished Educator sleepaway camp last month. He teaches science. I teach math. We set those differences aside and found a connection. I use multimedia in my curriculum. Greg uses video for assessment in a way I found compelling.

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How Long Is a Piece of String? book. Read 22 reviews from the world's largest community for readers. In this sequel to Why Do Buses Come in Threes?, you ...

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Conceptual understanding

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Our unit is change.....Using transformations, parallel lines cut with transversals.

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Best websites for teaching and learning math

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Best websites for teaching and learning math

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Recently in our WeAreTeachers HELPLINE group on Facebook, the conversation turned to the best math websites for teaching and learning math. What a treasure trove! We've gathered all the links and included a short description of each math website, along with a grade level recommendation and the cost, if any. Our list covers grades K-12 and is full of resources, games, freebies, and innovative programs.

Here are the best math websites, according to teachers.

Best Math Websites - Comprehensive Math Programs
These websites provide standards-based math curricula, practice activities and games, assessment tools and instructive insights, and professional development.
From McGraw-Hill, a web-based assessment and learning system that uses adaptive questioning to determine students' needs. It also instructs students on topics they are most ready to learn.
Cost: $
Along with textbooks, Art of Problem Solving has a stable of robust online resources, including videos, math problems from math contests, and online classes. Also features after-school enrichment resources.
Grades: 2-12 Cost: $
BuzzMath focuses on helping middle schoolers practice their math skills. It contains high-quality problems. It gives immediate and detailed feedback, letting students progress at their own pace. Randomly generated values let students retry problems to obtain mastery. Teachers also receive detailed results that help them guide and monitor student progress.
Grades: 6-9 Cost: Free demo; $ subscription for students and families.
This resource from England provides math videos, math practice questions, and worksheets with answers.
Grades: K-12 Cost: Free
This National Science Foundation-funded program helps students strengthen math skills, inspires a growth mindset, and encourages critical thinking. Students will learn to solve problems and explain their thinking using mathematician George Polya's four-step approach.
Grades: K-12 Cost: Free trial; $
An award-winning series of math apps that harness the power of digital tools to create a better, deeper, more fun learning experience. Blogs, such as "Making Math Social" and "Saying No to Math Anxiety," are included as resources for teachers and parents.
Grades: K-6 Cost: Free trial; $
An adaptive learning platform designed to complement classroom instruction and deliver results. Includes resources for teachers, student data reports, and instructive insights.
Grades: K-8 Cost: Free trial; $ subscription
Online learning digital curriculum for primary or supplementary instruction. Give students the support they need exactly when they need it.
Grades: K-12 Cost: $
This site provides e-textbooks, answer keys, video lessons, and printables for students and teachers of algebra 1 and 2, geometry, and trigonometry.
Grades: 8-12 Cost: $
We love the friendly competition and game-based content offered by First in Math. Kids gain skills practice and fluency as they play games targeted toward fact proficiency, automaticity, and logical thinking.
Grades: K-8 Cost: Free trial; $
Allows kids to practice math at their own level and pace. Has more than 30,000 math questions, starting with a diagnostic that assigns material at just the right level. Front Row also features lessons, assessments, and reports for teachers.
Grades: K-9 Cost: Free for teachers; $ for upgrades and other features
GregTangMath strives to provide unparalleled math lessons for students as well as professional development for in-service teachers. Games, puzzles, and other resources, like free downloads, worksheets/word problems, math centers.
Grades: K-6 Cost: Free
This site, from the National Council of Teachers of Mathematics (NCTM), features complete lesson plans, mobile games for students, interactive activities, and brain teasers.
Grades: PreK-12 Cost: Free
High-quality educational resources for teachers and students. Excellent math tasks, videos, lesson plans, and problem-based curriculum modules.
Grades: 6-8 Cost: Free
Istation makes personalized learning easy with computer-adaptive instruction, assessments, personalized data profiles, and teacher resources. Includes d igital lessons and face-to-face teaching strategies.
Grades: PreK-8 Cost: $
Make math about more than numbers! Engaging items, real-world scenarios, and unlimited questions. Individualized math practice. Teachers can choose the strand and set up students to work independently.
Grades: K-12 Cost: $
Khan Academy is on a mission to give a free, world-class education to anyone, anywhere. Their personalized learning resources are available for all ages. Video learning segments are followed by practice activities.
Grades: K-12 Cost: Free
Cloud-based curriculum for K-12 students, focusing on supporting both traditional and blended classrooms.
Grades: K-12 Cost: Free; $ premium version
Online learning space that is engaging, supportive, and designed to get kids interested in math while teaching state standards.
Grades: K-12 Cost: Free trial for teachers and families; $ subscription
Award-winning program finds and fixes learning gaps with the power of personalized learning. Three-pronged approach features personalized learning, pinpoint assessments, and interactive classroom.
Grades: K-8 Cost: Free version includes all curriculum, one test per year, and basic overview of student progress; $ for personalized learning license
Stepping Stones, from Origo, is a unique and comprehensive curriculum that combines print and digital materials. It features problem-solving activities, strategies, and practice. Teachers also have access to a professional blog that provides advice and support.
Grades: K-6 Cost: $
This organization helps students in low-income communities, together with teachers and families, harness the power of digital learning platforms to raise educational outcomes. The program features school workshops, instructional coaching, and professional learning communities.
Grades: K-12 Cost: $
Math games that tackle more than 1,200 crucial math skills in a fun and engaging way.
Grades: 1-8 Cost: Free for teachers; $ for family subscription
Interactive, game-based learning world that motivates kids through rewards. Features include daily challenge, step-by-step lessons, and parent connections.
Grades: K-5 Cost: Free; $ monthly fee
Boost confidence, increase scores, and get ahead. Fun for enrichment or regular practice.
Grades: K-5 Cost: Free basic plan; $ premium plan
Math games that make learning fun! Engaging, evidence-based, adaptive learning. Focus on specific skills, target interventions, and make assessment easy.
Grades: K-5 Cost: Free trial; $ subscription
Woot Math offers adaptive practice for teaching rational numbers and related topics, such as fractions, decimals, and ratios.
Grades: 3-7
Cost: Free tier for teachers; additional features available for extra cost

Personalized math curriculum that includes digital lessons and small-group instruction. Also has online modules, workbooks and answer keys, and professional development.
Grades: K-5 Cost: $
Best Math Websites - Interactive Tools to Use in Instruction
These sites offer engaging videos and tools to use in your daily math instruction.
Engaging animated learning videos, games, quizzes, and activities to encourage kids on their unique learning path.
Grades: preK-8 Cost: $
An online graphing calculator that students can use for free. Includes a teacher-centric activity builder for creating digital math activities.
Grades: 9-12 Cost: Free
Use hip-hop to teach math! Flocabulary offers songs, activities, and videos.
Grades: K-12 Cost: Free trial; $ subscription
Another graphing calculator for functions, geometry, algebra, calculus, statistics, and 3-D math. Includes practice sheets.
Grades: 9-12 Cost: Free
You know it; your kids love it. Why not use it to teach math? Engage your students with this game-based classroom-response system played by the whole class in real time. Multiple-choice questions are projected on the screen, then students answer with their smartphone, tablet, or computer.
Grades K-12 Cost: Free 30-day trial; $ subscription
Run by the University of Regina in Canada, this site offers free resources for math teachers and their students, including a database where users can search for the answers to math questions. Their Mathematics with a Human Face page includes information about careers in mathematics as well as profiles of mathematicians.
Cost: Free Grades: K-12
Teachers know that one of the best ways to make sure learning sticks is through song. Numberock features ad-free music videos of songs about math topics, like fractions, money, and integers, produced by an Emmy Award-winning studio. Numberock also has anchor charts, worksheets, comics, games, and more.
Grades: K-5 Cost: Some videos are free; free trial
Best Math Websites - Games and Activities for Students
Interactive websites that provide students with instruction and independent practice.
Two users play a game in which each player tries to connect four game pieces in a row (like game Connect Four). The players answer math questions to connect the pieces. Teacher chooses how much time each player has to answer, the level of difficulty, and the type of math problem.
Grades: 2-8 Cost: Free
Just like it sounds, this game challenges students to beat a calculator! Features step-by-step directions for performing functions quickly.
Grades 3-8 Cost: Free
Yes, math games can be cool! Check out the hundreds of games on this site and on Coolmath4kids.
Grades: K-12 Cost: Free; $ ad-free version
Figure This! is a site designed to encourage families to practice math together. It includes fun and engaging math games and high-quality challenges. It even offers challenges in Spanish.
Grades 6-8 Cost: Free
This math game serves a dual purpose. Students practice multiplication and pre-algebra math. For each answer they get right, the World Food Programme donates 10 grains of rice to help end hunger.
Grades: 3-7 Cost: Free
Funbrain has been helping students learn key math concepts and develop crucial skills since 1997. Students can choose from a slew of games. The best part? It's all free!
Grades: preK-8 Cost: Free
Hotmath provides homework assistance for high school and college students, using "worked out" examples of math problems.
Grades: 9-college Cost: Free
Your students will love fun math games like Speed Math Deluxe, Mystery Math, Place Value Game, and more.
Grades: 3-11 Cost: Free
Organized by grade or subject, your students can play math games and get homework help.
Grades: preK-7 Cost: Free
In-depth lessons with videos, guided practice, interactive self-tests, and more.
Grades: 5-12 Cost: Free
More than 425 math games, logic puzzles, and brain workouts for students to practice their math skills.
Grades: 1-6 Cost: Free
(formerly Mr. Nussbaum Math)

Nearly 100 original math games, workshops, and practice modules, as well as math printables!
Grades: 1-6 Cost: Free
This interactive, online tool helps students master basic facts. Set up as a whole-class or small-group competition, students earn ninja cards and track results on a ninja scoring poster. Two board games that teach operations are also available for purchase.
Grades: 2-8 Cost: Free
This is a free intervention tool designed to fill gaps in students' mental calculation skills and empower them with number fluency. Students can earn ninja belts of different colors for their skill level.
Grades: 2-8 Cost: Free
From PBS Learning Media, middle schoolers will love this entertaining video blog. Not only does each episode cover Common Core Standards, it makes math learning culturally relevant with pop-culture references.
Grades: 6-9 Cost: Free
Students can create study flashcards, play learning games, practice skills, collaborate with other students, and more.
Grades: 5-12 Cost: Free
Another resource to help students build fact fluency. Each game is tailored to students' ability levels.
Grades: 2-6 Cost: Free trial; $ monthly subscription
Tons of fun and educational online math games, from basic operations to algebra and geometry.
Grades: K-6 Cost: Free
Simple math test activities for teachers and students, from beginning math operations to calculus. You set the skill level, how many problems, and time limit. A report, which tallies right and wrong answers, is provided after each quiz.
Grades: 3-12 Cost: Free
How would your students like to learn multiplication while shooting hoops? They can do that and more at Toy Theater, which teaches early math concepts through game-based learning.
Cost: Free Grades: K-5
Xtramath is like a daily math vitamin. An interactive online tool that helps students practice and master basic arithmetic facts, it's quick and easy to use. Weekly emails provide progress reports for teachers and parents.
Grades: K-8 Cost: Free
Best Math Websites - Resources for Teachers
Sources for teachers that provide lesson-planning resources and professional development materials.
Math worksheets for just about any area of study. Free downloads. Good for planning lessons, review, and independent work.
Grades: K-6 Cost: Free
For teachers of pre-algebra through calculus. Create the math worksheets you need, exactly how you want them, in minutes. You can also create customizable homework, quizzes, and tests.
Grades: 8-12 Cost: Free
A creative solution that aims to revive students' passion and interest in math. Mashup Math has a library of 100+ math video lessons as well as a YouTube channel that features new math video-lessons every week. A free e-book of math challenges is also available.
Grades: K-8 Cost: Free
Dynamically created math worksheets for students, teachers, parents ... anyone!
Grades: K-10 Cost: Free
With their interesting lesson plans and quirky questions (e.g., "Do people with small feet pay too much for shoes?"), math class will never again be boring.
Grades: 6-12 Cost: $ subscription
Tools for math teachers, including bell-ringers and drills, math tools and manipulatives, question generators, printables, and puzzles.
Grades: K-12 Cost: Free
This National Science Foundation-supported project provides a large library of uniquely interactive, web-based virtual manipulatives and concept tutorials for math instruction.
Grades: K-12 Cost: Free
TopMarks is a UK-based site that provides a database of resources for teachers as well as online learning games for students.
Grade: PreK-8 Cost: Free
More than 1,500 video lessons ranging from middle-grade math through algebra 2.
Grades: 6-12 Cost: Free
For more ideas, check out our collection of math articles.
What's on your list of best math websites? Share your ideas in our WeAreTeachers HELPLINE group on Facebook.

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The Best Websites for Teaching and Learning Math

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Recently in our WeAreTeachers HELPLINE group on Facebook, the conversation turned to the best math websites for teaching and learning math. What a treasure trove! We've gathered all the links and included a short description of each math website, along with a grade level recommendation and the cost, if any.

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At the heart of the IB is the Learner Profile, a long- term, holistic vision of education that underpins all three programmes and puts the student at the centre of teaching and learning.

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by Terry Heick

What is The Feynman Technique?

In short, it's a simple approach to self-directed learning that is based on distilling what you know. Albert Einstein is often credited with having said that (paraphrasing) "you don't know something well if you can't explain it to a child."

And that's the Feynman Technique in a nutshell.

The technique is named after Richard Feyman (May 11, 1918 - February 15, 1988) an American theoretical physicist, who was involved, among efforts, in the Manhattan Project and has a background in doing exactly what you might expect: teaching himself complicated ideas.

For this post, we're mostly interested in his contributions to learning itself, and Wikipedia helpfully offers some background.

When Feynman was 15, he taught himself trigonometry, advanced algebra, infinite series, analytic geometry, and both differential and integral calculus. Before entering college, he was experimenting with and deriving mathematical topics such as the half-derivative using his own notation. He created special symbols for logarithm, sine, cosine and tangent functions so they did not look like three variables multiplied together, and for the derivative, to remove the temptation of canceling out the {\displaystyle d} 's. A member of the Arista Honor Society, in his last year in high school he won the New York University Math Championship. His habit of direct characterization sometimes rattled more conventional thinkers; for example, one of his questions, when learning feline anatomy, was "Do you have a map of the cat?" (referring to an anatomical chart).
Learning By Simplifying: How To Use The Feynman Technique
There is, of course, a difference between knowing something and knowing the name of something and that's where understanding types of knowledge is crucial.

In order to understand something, you should be able to explain it briefly and accurately but in order to do that, you need to understand the kinds of things a person can and might know (declarative knowledge versus procedural knowledge, for example).

That's a topic for another day. Today is about Feynman and his approach to learning: If you can't explain something to a child, there's a chance you don't understand it well and by coming to be able to explain it briefly and accurately, you'll be learning.

The video above from Thomas Frank at collegeinfogeek.com offers a nice overview of the Feynman Technique and below, I itemized the steps of this simple approach to learning.

Note, I did take some artistic liberty by focusing a little more on documenting the process of learning by adding in the documenting how your knowledge has changed (part of step 4) rather than simply on continuously restating your understanding in simple terms. If you want to stick purely to the original form of the Feynman Technique as the good scientist intended, refer to the video itself more than my crude itemizing below.

The 5 Steps Of The Feynman Technique 1. Clarify exactly what you want to learn
Clarify the concept you want to understand and write it at the top of a blank piece of paper. The more specific you are, the cleaner and more efficient the rest of the learning process can be.
2. State (and self-assess) current understanding
In the plainest language possible, write down an explanation of the idea as if you were teaching it to someone who does not understand it at all

Note, it's fine to start out with a broad summary and then get more specific, working through examples, scenarios, or other subtleties of the concept. Simply stating it broadly isn't enough to fully demonstrate 'understanding' but rather is a kind of 'foothold' to work from as you do demonstrate that understanding.
3. Acquire new knowledge
If you can't explain it fully, go back and reread, research, and relearn source material until you feel more or less confident in your explanation.

Note, if we lack expertise it can be difficult to know what we do and don't know so this part isn't perfect. However, as you become accustomed to the technique-and self-directed learning in general-you can develop a better instinct for what you do and don't understand-and of the latter, what's most important and where you should start.
4. Document new knowledge and clarify new understanding
As you gain new knowledge, reflect on and document new knowledge-especially how your understanding has changed.

Creating visuals, concept maps, and any of the various types of analogies is a useful way to clarify your own thinking. In short, you're trying to-with both accuracy and precision-demonstrate a more or less complete understanding of the topic you're trying to learn with the Feynman Technique.

As your understanding changes, your demonstration of that understanding should change. This will both deepen your understanding of the topic as well as illuminate the learning process itself (which can carry over into learning about new topics).

5. Restate evolved understanding (i.e., as compared to step 2)

Once you've 'done the work' of learning, try to-without checking your paper or other research notes or documentation-state your understanding again-from scratch and without reference. If you can't, go back and repeat steps 3 through 5.
Learning By Simplifying: How To Use The Feynman Technique

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by Terry Heick What is The Feynman Technique? In short, it's a simple approach to self-directed learning that is based on distilling what you know. Albert Einstein is often credited with having said that (paraphrasing) "you don't know something well if you can't explain it to a child."