Which One Doesn’t Belong? K-12 Critical Thinking and Problem Solving

Which One Doesn't Belong? Math sets

What it is: Which One Doesn’t Belong? is a site I learned about from @TeamBaldwin today. This math site is for students of all ages and challenges them to look at a set of four images and determine which image doesn’t belong and justify their answer. The best part of this site is that each problem has multiple correct responses that can be justified. Students have to think through the differences that they see and then make logical decisions and be able to explain it to others. There are three different categories for Which One Doesn’t Belong including: Shapes, Numbers, Graphs and Equations.

How to Integrate Which One Doesn’t Belong? in your classroom: My favorite part about this site is that there are multiple answers for each set. Students can see how perspective and which attributes you are looking at can change the answer. The site is a great catalyst for critical thinking and problem solving in math (or any) class. Put a problem set up on a projector as a math class starter and ask your students to independently choose their answer and be ready to justify it. Then, as a class, discuss answers. After students have done this once, challenge them to find as many possible answers as they can independently before sharing responses. This site would be a great tie-in with the humanities to discuss perspective and vantage point. Even in something that feels as static as math, perspective can actually make any problem quite dynamic.

Yesterday, @TeamBaldwin used the site this way:

Which One Doesn't Belong? Math setsWhich One Doesn't Belong? Math setsWhich One Doesn't Belong? Math sets

This is a class of kindergarten and first grade students! @michellek107 will be blogging more about the class experience on the class blog, Architects of Wonder if you’d like to read more.

Tips: The graphs and equations appear quite challenging, but even young students can begin making observations about the types of graphs that could lead to some higher-level math discussions.

Brown Sharpie: Mathematical Cartoons Inspired by Sharpie Fumes

What it is: Math geeks, eat your heart out…Brown Sharpie is for you!  I found Brown Sharpie by accident today as I was perusing the app store in iTunes.  Brown Sharpie is a collection of “mathematical cartoons inspired by sharpie fumes” drawn by Courtney Gibbons.  Gibbons is an aspiring mathematician and the cartoons were created as she completed her undergraduate and graduate degree.  Many of the cartoons reference higher math and may be too complex to use in the k-8 classroom.  There are a few here and there that could be used with younger students with a little explanation.  High school, college math students and math geeks are the main demographic for these cartoons. The cartoons are shared blog-style so you can search through them using the “next” and “previous” buttons or you can view by tags using the “view by…” word cloud in the right side bar.

             

How to integrate Brown Sharpie into the classroom: The Brown Sharpie cartoons would be a fun start to math class.  Put a cartoon up on a projector-connected computer each day for a little math humor to kick off class.  The cartoons will give you the opportunity to discuss current math topics as well as give an introduction to math concepts not yet touched on.

Why not hold your own Brown Sharpie day?  Give each student a brown fine-tipped sharpie to create their own math cartoons?  These can be shared on a class blog, website or wiki.  This will help your visual learners and artists think about math in a whole new way!  Students of any age can create a Brown Sharpie cartoon of their own!

In addition to the blog, Brown Sharpie is also a free app in the iTunes app store.

Tips: Some of the cartoons are PG-13 with alcohol or relationship references.  Best to preview the cartoon before displaying before your class. 🙂

Please leave a comment and share how you are using Brown Sharpie in  your classroom!

On Demand Learning: Classroom Optional (Khan Academy and Academic Earth)

What it is: Tonight I was talking education with a fun group that is helping me think through my school design.  As we were talking one of the participants mentioned Khan Academy…some of the teachers in attendance had never heard of it.  I sometimes forget that not everything is common knowledge and even if it is common knowledge to most, there are still those who can benefit from the mention!  Khan Academy was started by Salman Khan quite by accident.  He tutored his cousins in math and when he moved away from them, they still requested support.  Sal began making algebra videos and uploading them to YouTube for his family, it has grown to over 2,100 videos and 100 self-paced math, science, and history exercises for students.  The library is extensive and comprehensive including algebra, arithmetic, banking and money, biology, brain teasers, calculus, California standards algebra, geometry, chemistry, cosmology and astronomy, credit crisis, current economics, developmental math, differential equations, finance, history, linear algebra, organic chemistry, Paulson bailout, physics, pre-algebra, pre-calculus, probability, statistics, trigonometry, valuation and investing, venture capital, and capital markets.  It is a pretty impressive collection!  I really like these videos because they provide students with on-demand learning and present the learning in a way that appeals to the visual and auditory learner.  The experience is so much richer than a textbook can offer. It is like having your own personal tutor.

Academic Earth is another extensive video library that lets students (and adults) take video courses from the worlds top scholars all in one place…for free!  The mission of Academic Earth is to give everyone access to a world class education.  Subjects covered by Academic Earth include art, architecture, astronomy, biology, business, chemistry, computer science, economics, education, electrical engineering, engineering, entrepreneurship, environmental studies, history, international relations, law, literature, mathematics, media studies, medicine and health care, philosophy, physics, political science, psychology, religious studies, test prep, and writing.  Students have access to the learning happening at Berkley, Columbia, Harvard, Khan Academy, Maryland, Michigan, MIT, Norwich, NYU, Princeton, Stanford, UCLA, UNSW, USC, and Yale.  Did I mention all of that learning is free?  I know, amazing!

How to integrate Khan Academy and Academic Earth into the classroom: Both Khan Academy and Academic Earth provide students with opportunities for on-demand learning in their areas of interest or their areas of weakness.  Students can use these resources to support the learning happening in the classroom and to fill any gaps that students may have in their learning.  Video is a powerful medium because it appeals to a wide range of learners and makes it easy to pause, rewind, review, and share that learning.

Khan Academy would be a great tool to use for the “Fisch Flip” where the homework is to watch the lesson on video and class time is spent on working through the problems together.  Let that sink in…makes more sense doesn’t it? Students get support where they need it most, in the follow through and practice of the learning.

Academic Earth provides students with the opportunity of pursuing their passions, getting a feel for what type of study they would like to pursue in a university, and support learning.

Do you have students that could use additional challenge and are constantly searching for more learning? Set up an extended learning center in your classroom where students who need that challenge can self direct and extend their learning by using Khan Academy or Academic Earth.

Tips: Khan Academy is a great resource to pass on to families, parents are often looking for ways to supplement and support the learning happening in the classroom.  Math in particular is a challenge as many parents did not feel successful enough in higher math themselves to help their children.

Please leave a comment and share how you are using Khan Academy and Academic Earth in your classroom!

HippoCampus

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What it is: HippoCampus is a website with incredible vision.  The goal is to provide high-quality multimedia content on general subjects to high school and college students free of charge.  Subjects on HippoCampus include algebra, American government, biology, calculus, environmental science, physics, psychology, religions, statistics, and US history.  Each of the subject has a large library of multimedia content from students to learn from.  HippoCampus was designed as part of the Open Education Resources, a worldwide effort to make education available equitably to everyone.  Each lesson includes multimedia lessons, the text of the lesson, and related resources.  I believe the HippoCampus model will be the textbook of the future.  Students are able to learn at their own pace, pausing, reviewing, and receiving instruction on demand.

How to integrate Hippo Campus into the classroom: HippoCampus has an incredible library of content for teaching and learning.  Use the multimedia lessons in place of traditional textbooks or as a supplement to your current curriculum. Teachers can build their own HippoCampus homepage where students can access specific lessons targeted for them.  You can even create custom announcements to be displayed to students.   Although HippoCampus was designed with high school and college students in mind, many of the multimedia presentations could be used to teach middle school students as well.

Tips: HippoCampus uses Adobe Flash and QuickTime.  Make sure that you have each on your computers before using HippoCampus.

Leave a comment and tell us how you are using HippoCampus in your classroom.

Mathway: Step-by-Step Math Problem Solver

What it is:  Mathway is a website that I initially didn’t appreciate.  The site is a step-by-step problem solver and my immediate reaction was: so we will be helping students cheat?  But, the more I explored the site, the more I saw its value.  The beauty of Mathway is that it is not just a site where students enter an equation and get an answer, the site shows the process of getting to that answer.  It shows them the step-by-step process of obtaining the correct answer.  Mathway has a step-by-step problem solver for basic math, pre-algebra, algebra, trigonometry, precalculus, and calculus.  It also has a graph section and a math glossary.  

 

How to integrate Mathway into the classroom: Mathway could be very valuable to students who have notebooks full of notes but get home to solve the problem and are still stumped.  I like that it doesn’t just give students the final answer but leads them to the answer, showing them the process.  This would also be very useful in a large class.  If students are struggling with a problem, they can visit the math center (a computer with Mathway) instead of wasting time waiting for a teacher explanation.  

 

Tips:  Let parents know about , you will be saving them from the frustration of having to dig into the recesses of their mind to remember how to do some of this, and saving yourself from re-explaining the correct method after parents have guessed and taught students the wrong way.

 

Leave a comment and tell us how you are using Mathway in your classroom.

GeoGebra

 

What it is: I’m not generally one to get excited about math especially algebra, geometry, and *uggh* calculus. But, I think if I had access to a tool like GeoGebra I might have enjoyed them (or at least understood them) more. GeoGebra is a free dynamic geometry system that lets students complete constructions with points, vectors, segments, lines, conic sections, and functions and change them dynamically afterward. Equations and coordinates can also be entered directly; this means that GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. (If you didn’t catch that you are not a high school math teacher *wink*). If you are a high school or college math teacher or know someone who is…that description just made you feel a little excited. GeoGebra is a free multi-platform download.

How to integrate GeoGebra into your curriculum: Use GeoGebra to help your students understand complicated or abstract math concepts. This software is amazing for your visual learners…again a reason this should have existed when I was in school! Allow your students to explore math concepts with this software and to practice their learning. You can also use GeoGebra to create dynamic math worksheets for your students. Very cool!

Tips: Make sure to check out the examples section for some great GeoGebra uses. You can also attend free online workshops to learn how to use GeoGebra. For some great ideas and further explanation of GeoGebra check them out on Wikipedia.

Please leave a comment and share how you are using GeoGebra in your classroom.