3D QR Codes

QR Codes are all the rage right now in education.  When I was at NETA this year every other talk was about how they were using QR codes in the classroom.  This is hopefully my last post about QR codes, but I found this one quite extraordinary!

This is a QR sculpture in which between 12 and 1 o'clock when the sun is hitting at the right angle, then the QR code reveals itself and then you scan the shadows with your smartphone QR scanner.  I was wondering how hard it would be to build your own QR sculpture, or make an adjustable one where you could change your QR code for different websites for education.

Better question, what if your school had something like this outside their building where parents could scan the QR code from there car with information about the school such as closings or delays.  Here is the video for the one in South Korea.

QR codes are a great way to get students interested in mathematics.  At NETA I watched a presentation on how she used QR codes to do better on NESA math tests, which was a very interesting way of having the students get excited for testing.

Create Debate

I created my own debate and it can be found here: http://new-to-teaching.createdebate.com/debate/show/Going_1_to_1

I was very doubtful on how it would look, but it turned out really well.  My question was posed and if you click the link at the top you can add your own argument.

If you used this in the math classroom I could see very useful ways of creating your own debates and having your students use this well.  Students could either create their own questions or the teacher could post questions or exploratory assignments for the students to look up then discuss.  Very cool!!  Here is the link for the website: http://www.createdebate.com/

Problem Based Learning

Problem based learning approach is largely attributable to the fact that their process is designed to stimulate student inquiry. Additionally, the process can be applied to any project in any subject, which means there is a consistent approach across grades and subject areas.  Featured below is a step-by-step guide to problem based learning, there are multiple ways of PBL.

• State Standards: every project should start with some standard the students are suppose to hit, you can make a rubric that students should be able to tell which ones they are covering.
• Critical Friends: students and teachers should participate in a peer review or "critical friends" before they launch a project and have a session with colleagues for feedback about the academic rigor of the project.
• Entry Event: Teachers introduce each project with an entry event that serves several purposes: to hook the students and get them engaged in the content, provide an example of what to expect, and introduce key vocabulary.
• "Need-to-know" list: keywords that should prompt students to identify new concepts they'll need to learn and help make connections.
• Rubric: The rubric is an essential tool for maintaining transparency for students.  Teachers design rubrics to define all the desired learning outcomes for a project.
• Group Contract: Individual accountability is a critical component for successful PBL where students use group contacts to document expectations for each team member.
• Research and Collaboration: students work together to figure out what their final product is going to be and how to acquire the knowledge they need to complete it.
• Assessment and Adjustment: Teachers track student progress to make sure no student is falling behind.
• Presentations: Verbal communication, public speaking, and other important nonacademic skills are honed in this process.
• Final Assessment: Students are graded on the work they have done according to the rubric and group contracts they signed.
Creating an environment that makes students feel welcome and able to complete a problem based learning classroom is the ideal setting since this is the type of atmosphere most students will be working in when they get older.

Women in Math

I would list some women that made significant contributions to mathematics, but the list would be incredibly long and no one wants to read all that information.  Here are two really good sites about women in mathematics, since women were not allowed to practice mathematics at such a high level.  It is good to get girls involved in math and STEM as young as possible.

Hilda Geiringer was born in Vienna, Austria. She received her Ph.D. in 1917 from the University of Vienna with a thesis entitled "Trigonometrische Doppelreihen" about Fourier series in two variables. From 1921 to 1927 she worked at the Institute of Applied Mathematics at the University of Berlin. Her mathematical interests had switched from pure mathematics to probability and the mathematical development of plasticity theory.

Julia Bowman was born on December 8, 1919, in St. Louis, Missouri, to Ralph Bowers Bowman and Helen Hall Bowman. She studied with a tutor for a year, covering material from the fifth through the eighth grade. The tutor's claim that the square root of two could not be calculated to a point where the decimal would repeat itself fascinated her.  Her outstanding achievements and abilities were recognized during her lifetime. Robinson became the first woman mathematician to be elected to the National Academy of Sciences in 1975.

Listed below are two great resources for other women in math:
http://darkwing.uoregon.edu/~wmnmath/People/index.html
http://www-history.mcs.st-and.ac.uk/Indexes/Women.html

Creating Comic Strips

Why should students create comic strips?

• Provides another option for projects
• Allows for a lot of creativity
• Incorporates both visual and written information
• Can improve narrative writing skills
• It's fun!
Ideas for how students could use comic strips:
1. Students can illustrate a concept from class.
2. Students can retell a story they have read in class. (Such as Flatland.)
3. Re-enact famous scenes from math history.
4. How they use math in a daily basis.
5. Make a comic using vocab words for that week.
There are multiple links and one especially well done is a google hangout that I saw that creates comic strips using google docs.  The link is here: https://docs.google.com/presentation/d/16goLqOmvMd1jh29dcIQ-kDk0fo8AFaihfa2FYZDHn2o/edit#slide=id.ge66c43f_0_7

A great resource when using google docs to create these comic strips is: http://openclipart.org/

Thinking Mathematics!

Thinking Mathematics is an uncluttered and joyous approach to school mathematics from middle school, high school, and beyond.  The site is based on the material that appears in the book series Thinking Mathematics!

There are excellent newsletters that I have signed up for that gives out great resources and extra examples you may be going through with your own students.  Here is May's Newsletter: http://www.jamestanton.com/wp-content/uploads/2012/03/Cool-Math-Newsletter_May2012.pdf

There are links like a School Math Genius: Five Principles.  A Teacher's Guide.  Here is the first one from YouTube.

Here is a link to his page of his five principles: http://www.jamestanton.com/?p=1097

There are also thinking puzzles and cool math videos that make students think and problem solve.

A brief history of mathematics, professor Marcus du Sautoy argues that mathematics is the driving force behind modern science.  Ten fifteen minute podcasts that reveal the personalities behind the calculations from Newton to the present day.  How do these masters of abstraction find a role in the real world.

1. Newton and Leibniz
2. Leonard Euler
3. Joseph Fourier
4. Evariste Galois
5. Carl Friedrich Gauss
6. The Mathematicians who helped Einstein
7. Georg Cantor
8. Henri Poincare
9. Hardy and Ramanujan
10. Nicolas Bourbaki

Mullet Ratio

A lesson they will remember.

Urban Dictionary defines mullet ratio as a mathematical term used to describe how extreme a mullet hairstyle is.  It is found by comparing how long the hair on to of the head is compared to how long the hair hangs at the back of the neck.

The best way to see the lesson is read Mr. V's class here: http://mrvaudrey.wordpress.com/2012/05/03/the-only-lesson-theyll-remember/

So if you read the above link and found your way back here, there is one more thing I would add to the lesson and it would be to sort the pictures on a graph and it would be a graph with ratios compared to good ones, high ratios would be on one side, low ratios on the other.  It should come out to the better looking mullets have a close ratio and the outliers have worse mullets than any other.

A good extension activity would be to request iPads and have students find mullets: good ones, bad ones, and the truly awful ones.  Calculate and have the students have their own poster boards in groups and present their findings to the class.

Think Wrong

Trying to come up with ideas is tough, especially problem solving ideas in math especially.  The key to generating truly innovative ideas is learning how to challenge the status-quo, by thinking wrong.  It seems to students and parents that math shuts down imagination and that is how these ideas came to be is by someone imagining them.  In math it is OK to be wrong and as we get older we associate failing by being wrong.  Working within our comfort zone renders us unable to approach problems with a truly fresh perspective.

If teachers create a safe enough environment that is fun and loosely structured and encourage participants to question protocol on problems that require higher-ordered thinking.  Then we begin to see totally different equations than the ones in textbooks and possibly better equations that they may be able to use throughout their entire life.

End of the Year

It has been coming for months and the end of the year is apon us.  Most teachers now put it into cruise control and coast to the end of the semester.  Here are 12 effective end of the year activities to do with your students to motivate them to the end of the semester and get them prepared for the upcoming one. http://www.teachhub.com/top-12-effective-end-year-activities

By: Kim Haynes.

Let the kids teach the class.
Split the class into groups and assign each a specific topic you studied this year. Give them time to go over their topic and invent a good review activity, which they have to grade. You assess them on whether they get their facts straight and how effective their review activity is.

Have students write a children’s book.

When writing for younger children, your students will have to really simplify and emphasize the key elements of your course. This can serve as a great review and a fun way to integrate art into the curriculum. Students might write the children’s version of a Shakespeare play, a young readers’ version of the history of Ancient Egypt, or a picture book that illustrates the cycle of life.

Host a talk show or “expert” symposium.

Imagine an Oprah-style show on bullying or school violence as a way to discuss The Chocolate War. Or a discussion on “Great 20th Century Achievements in Science” featuring Albert Einstein, Neil Armstrong, J. Robert Oppenheimer, and Stephen Hawking – all portrayed by students. Put students in groups and have them research their topic, write a script on it, and present their show to the class.

Create a class scrapbook.

Let each student make a page. Offer some prompts (My favorite book we read…/The best experiment we did in Chemistry…/One thing I learned about myself…) and encourage students to include favorite class memories. Supplement with photos of students, the classroom, or class activities. Make a copy of the scrapbook for every student, or make an electronic scrapbook and take the opportunity to teach students how to use PowerPoint or another program.

Have students write letters to themselves.

Ask your students to write themselves a letter, reviewing the year and making “resolutions” for the next school year. Give them some prompts to write about: one thing they are proud of from this year, one thing they would like to do differently next year, one thing they want to remember, and so on. You can either mail these letters to your students just before the start of the next school year, or make arrangements with their next teachers to distribute the letters at the start of school.

Have your current students write letters of advice for the new students you will teach next year. What advice would they give on how to “survive” or do well in your classroom? What are the hardest parts of the course? Note – if you have any special traditions or “surprise” activities you don’t want students to spoil, make sure to tell them ahead of time.

Create a portfolio or profile for each student.

Work together with your students to develop an individual profile that highlights their work from this year. Depending on the level of your students, this may include samples of work, a self-evaluation, and a written teacher evaluation. If possible, make two copies – one for students to show their parents and a second copy for the student’s next teacher. Keep in mind: this activity works best when it relies on student work and self-assessment more than teacher comments.

Invite students to evaluate the course.

For older students, evaluating the course can be valuable on many levels. They may surprise you with their assessments of their own contributions and may have some good suggestions for ways to revise the course. Even better, you’re providing a good model for them, showing everyone can benefit from constructive feedback and all of us have things to learn.

Teach that fun unit you never have time for.

Most teachers have fun units or activities they can never find time for: why not do it now? Food math, logic puzzles, “Mythbuster”-style experiments, or lessons on advertising or political cartoons – these are legitimate educational activities with a high “fun factor” that will make it easier to hold students’ attention.

Go outside.

As the weather warms up, find a way to teach outside. Students can explore nature using math or science skills or write a poem about the weather. Got an activity that is messy or noisy? Doing it on the field is a great way to enjoy spring. Of course, students may get more rowdy outdoors, so make it clear that if they misbehave, it’s back to the classroom and normal (a.k.a. “boring”) assignments.

Put a new twist on skill drills.

Every teacher has skills or content they want students to practice – reading, writing, learning the Periodic Table, or memorizing the Pythagorean Theorem. Choose a specific skill and make it the focus on your lessons. Have a Reading Fair, declare Grammar Week, or hold a Math Theorem Memorization Contest.

Find a fun way to practice these skills – if your students need to improve their reading skills, can you allow them to read Sports Illustrated or X-Box: the Magazine? If they need more time on writing, have them write profiles of their favorite TV stars or even write their own autobiographies. Practice is easier than learning new material, but still a valid way to spend class time.

Do some good for the world.

Take this time to get involved with a cause that is meaningful to you or your students? Students can write letters to government leaders, organize fundraisers, or create pamphlets or flyers addressing a particular issue. You can build off world events, such as the Haitian earthquake or the Gulf Oil Spill, tackle an issue you read about during the year, or just ask students what issues matter to them.

Assessment III

Since apparently I get enough of assessments, since this is my 3rd post.  I will give you a few different examples in the math content area that you can apply right away to your math assessments.  This comes from www.jamestanton.com and it is a brief description of questioning techniques that we use and abuse in mathematics.

It is easy in mathematics teaching to focus on the "what" questions and miss "why" and "what if" questions.  There is no doubt that one needs to develop facility and ease with the basic skills of mathematics so that on is not always stumbling over small matters, but the richness and true utility of the subject comes from its conceptual structure.  Mathematical thinking should promote life skills.  The curriculum should be the vehicle for learning, not itself the goal of learning.  Mankind has not engaged in mathematics for thousands of years simply because it is useful, but because it opens to something more transcendental.  Why do math? Because it is beautiful!

In order to promote true conceptual understanding, one can ask "meta-questions." These come in a number of styles: Spot the error, head-on approach, explain, think before you leap, discover and explore, jolt, and pushing the boundaries.  Here are some examples to show you these questioning strategies that you can use as assessments that promote true understanding.  These are just a few of the ones that I chose, otherwise it would be 5 pages long and no one wants to see that.  Here is the pdf so you can view all of the resources: http://www.jamestanton.com/wp-content/uploads/2011/09/Assessment-Thoughts_APRIL-2012-Version.pdf

Elementary Math

Since it is my sister's birthday today and she is going to be a future elementary educator.  I have decided to dedicate this post to elementary teachers who are looking for materials or resources for elementary math.

Mathlanding is a resource and tools for elementary math specialists and teachers.  You can search by math topic and grade level.  You can find goodies for the classroom and professional development.  A team of math experts review and evaluate all resources and populate the site with thousands of engaging, high quality lessons, interactive games, activities, videos, and articles.

The professional development is the perfect platform to enhance the skills and knowledge of elementary math teachers.  http://www.mathlanding.org/

I used to love dinosaurs and most elementary schools are going away from using dinosaurs in the classroom, but coloring and doing math at the same time can't hurt.  This link takes you to pages of coloring math activities that feature dinosaurs.  http://www.enchantedlearning.com/subjects/dinosaurs/activities/mathcolor/

Another awesome page that includes math coloring pages is: http://www.coloringprintables.net/math-coloring-pages.html

Another great site is Mrs. Hughes' Place for numeracy teaching notes that has posters and handouts and the link can be found here: http://billsteachingnotes.wikispaces.com/Numeracy+Teaching+Notes

Personalized Feedback

When you are grading, no when you are going over tests do you run through the problems on the board for all the students to see, even the ones who got the question right?

No teacher has time to personalize feedback in math class.  Or do they?  If you record yourself when going through a test you can personalize each test as you go through the test.  You can say, "Wow, that was great on that question." or "Oh, you just forgot a decimal place." or lastly, "You need to explain more here on number 6, I did not get your thinking."  This not only personalizes each test, but your students get use to your thinking and knowing what you want to show on the test.  They can hear your thinking over and over again if they need to retake or take another test it would be a great way to study what they missed.

Since my HTML does not like me right now I will just copy the address to the video and article.
https://www.teachingchannel.org/videos/student-feedback-through-technology

This recording device was through an Apple computer and used for student's iPods.

Good videos are ones that instruct and engage at the same time, but not necessarily.  You can incorporate YouTube videos can use one to engage students and then one like Khan-Academy to instruct a lesson.  With a YouTube channel you can go ahead and favorite or add them to lists ahead of time for future lessons.  If students have emails you can add an unlisted video that you, and only the people you share the link with.  Here is the video where I found the all the information: http://www.youtube.com/watch?feature=player_embedded&v=odBHdujh0HM

10 ways you can use YouTube in the classroom:
• extend the walls of your classroom
• create interactive videos
• hook and engage your students
• student-paced learning
• student created video
• review for upcoming exams
• create extension opportunities
• help struggling students
A video on flips that may lead to a video on circles.

eThemes

eThemes is a source for content-rich, student safe online resources that will help you enhance your teaching and save you time.  eThemes provides free, fast access to over 2,500 collections of websites, on many different topics.  By researching and creating these resources for you, eThemes will save you the time trying to find a few websites that will meet your teaching needs.

This is for more middle grades mathematics, or at least most of the topics have to deal with the grades 4-8.  It even gives you a percentage on the side on what most fits the topic you chose.  For individualized lessons where you type in, for example, "perpendicular lines".  It will only show one answer, there are places where you can request more topics below.  Here is the link to the eThemes website: http://ethemes.missouri.edu/

I came across an interesting article from MindShift.  It gave instructions on how to create your own classroom textbook (with or without Apple).

As the open education movement continues to grow and become an even more rich trove of resources, teachers can use the content to make their own interactive textbooks.  It might seem daunting, but the availability of quality materials online and the power of tapping into personal learning networks should make it easier.  Here's how to create a digital textbook and strategies for involving the students in its development in three steps.

1. Aggregation: Gather all your sources of information.  The best way is through social bookmarking with great online tools such as Diigo, which allows you to bookmark sites that can be seen and shared online. Teachers can work with collegues within thier subject area departments and beyond the walls of the classroom to gather resources (such as Twitter which I gather most of my ideas!)
2. Curation: While gathering resources, the process of curation involves a deeper analysis of those sites to select the ones that have the most relevant material for a particular topic.  Use your syllabus or state standards to pick content for a unit of study.  Focus on essential questions to help you choose your resources.  Use web 2.0 tools to make your textbook engaging by using images, videos, and simulations.  Even putting them on online magazines such as LiveBinders and Scoop-it! (are great resources).
3. Creation: This is the most important part of the process.  You can create an online repository using a wiki digital tool that organizes your resources neatly.  One great tool now is Google Sites that allows you to create and share webpages, that have lots of customizable features.  You now have iBooks Author that you can also do it on.
I tried to minimize all the material to its basics, but check out the full article here: http://blogs.kqed.org/mindshift/2012/01/how-to-create-your-own-textbook-with-or-without-apple/

Urban Education

Culturally responsive management focuses on many teaching components, from as broad as choosing appropriate curricula and as specific as using congruent communication processes. Effective classroom management also involves the utilization of many essential research-based pedagogical processes as well as the ability to respond appropriately to the emotional, social, ethnic, cultural, and cognitive needs of students. Effectively managing students generally involves the ability to develop a classroom social environment in which students agree to cooperate with teachers and fellow students in pursuit of academic growth. It is a complex process that involves much interpersonal and pedagogical awareness and application of strategies in these two realms. In truth, most researchers and teachers may agree that managing student behavior while maintaining an appropriate learning environment is as much art as it is science. Researchers have addressed both of these views of management in studying students’ and teachers’ behaviors.

http://www.sagepub.com/eis/Brown.pdf

Family Feud

I have recently found this great way to assess understanding of concepts and math vocabulary.

Split the class up into groups of 4-6. Each group gets a set of small cards which each have on them one maths related word. The first thing they have to do is write on each card, under the math related word which is at the top, three words that people will not be allowed to use when describing the top word. For example, if the top word is circumference then three words the team could write underneath could be circle, perimeter and length. The idea is to make the describing of the top word as tricky as possible. The words that they can’t use when describing the top words are called Taboo words.
The sets of cards are then passed onto another group and one person in the group gets 1 minute to describe as many of the top words as possible to their group colleagues without using the taboo words. The teams get a point for each correct word they guess. Each team has a go and the scores added up at the end to identify the winning team. You can do a tie-breaker round if necessary.
There are lots of variations you could do of this game and it does seem to really engage the kids and is an excellent way to revise key vocabulary and assess conceptual knowledge.  You can create this variation into a Family Feud where different classrooms come up with the next classrooms list for a review game where you have to find object describes the word best.  This can be as a class or as small groups like the ones mentioned above.  You can find a link to the original article here: http://www.greatmathsteachingideas.com/2010/06/17/taboo-words/#comment-2843
Great Maths Teaching Ideas is a great place to get great teaching ideas for math teachers.  Happy Teaching!

Alice

Alice in Wonderland got its start as a simple story, told by a mathematics professor to a colleague's daughter.  It's a strange story that seems to be the result of a drug trip, but is actually a scathing satire of the new-fangled math that the professor was seeing invade his area of study.  There are many different guides to the math of Alice in Wonderland.  Here are some great sites that you can get for free, that you can read to get a better understanding of Alice in Wonderland.  Or read as a class to gain math insight from students in the class.

http://io9.com/5907235/a-math+free-guide-to-the-math-of-alice-in-wonderland?utm_medium=referral&utm_source=pulsenews
http://www.maa.org/devlin/devlin_03_10.html
http://www.slideshare.net/breaker561994/math-in-alice-in-wonderland-chapters-4-6-presentation
http://www.npr.org/templates/story/story.php?storyId=124632317
http://www.nytimes.com/2010/03/07/opinion/07bayley.html?pagewanted=all

There are other great books out there that may more fully describe each mathematical encounter Lewis Carrol came in contact with during the book Alice in Wonderland.

Prediction (3 Ways)

1.) Just having students predict answers to math problems is a way of creating more meaningful learning, prediction can be a useful strategy in successful teaching.  I was reading a publication about predicting mathematical creativity in students.  The study examined a number of cognitive factors that may predict creative ability in mathematics.

2.) Data analysis revealed that mathematical ability is the most fundamental of the components under investigation for predicting mathematical creativity. Since creativity depends on the amount of ideas that are available for recombination (Sheffield, 2009), if an individual has a limited domain knowledge then he/she will have fewer resources to draw from  and to form new ideas. In contrast, general psychological factors as working memory, intelligence, speed and control of processing are not valid predictors of mathematical creativity.

3.) Discovering Math: Prediction and Probability — From likelihood to frequency to prediction, introduce
young students to the basic concepts of probability.

It will take you to the lesson of discovering math using prediction and probability.  It is a great resource for anyone who is going to teach probability.

I saw this resource a teacher had on their page and it seemed interesting.  Letting their students on Facebook.... (sort of).  Students love social media, but most schools have policies that restrict student access of Facebook.  I have had students use a template I created in pages and in word as a work around.  This project works great when students are conducting work on biographies of people of a particular era.

You could use many different topics, especially what you are covering in math class would be a good tie in with the social presence of that era.  You could even have a wall hang where you assign students to develop the persona of each mathematician and have them write on each others Facebook pages.

Here is the link for the page, it is a history page, but would be a great addition to any math classroom.

http://wikihistory.wikispaces.com/Project_Ideas

Below features some of the outlines and individuals they had to choose from in the assignment.

Math Reasoning Inventory

Math Reasoning Inventory helps teachers find out what your students really understand about math.  It focuses on students' strategies, understandings, and misconceptions.  Teachers can learn how students respond to questions to standards.  (MRI) is an online formative assessment tool designed to make teachers' classroom instruction more effective.  An instant report can be used to inform instruction, monitor progress, and identify students who would benefit from intervention and communicate with parents.  The MRI interview reveals strategies to students that reason with whole numbers, decimals, and fractions.

There are multiple levels that you can sign-up for the first is free.  It also allows up to 160 individual students you can use it with.  Here is the link: https://mathreasoninginventory.com/Home/Index

TED-Ed

One of my favorite TED talks is about how algorithms shape our world.  It is a great video for people who have their major or are just getting interested in math.  TED-Ed uses engaging videos to create customized lessons.  You can tweak or completely redo any lesson featured on TED-Ed.  You can also create lessons from scratch based on any video from YouTube.

You have a lesson title that you can choose, play the video while working through the lesson.  You can also flip the lesson that turns your video into a customized lesson that can be assigned to students or shared more widely.  You can add context, questions and follow-up suggestions to any video on TED-Ed or YouTube.

So you watch the video, then your students could take the quick quiz on the whiteboard.  Then think questions that are short answer questions.  Then dig-deeper where you can have essay questions or research places you can visit for your students to explore.

Lurking

Learning is a process. Learning is different to all of us. Approaches to how we as individuals learn is unique and for those critics and pundits ‘out there’ who continue to perpetuate the myth that unless one is contributing back, one isn't learning, well simply put … I have a problem with you.  As I see it, as we continue to proliferate the ways in which we can in fact contribute and/or collaborate, we will be forced to make ‘learning style’ related decisions on when we have the time and capacity to contribute and/or collaborate versus lurking.
Lurking can and should be thought of in better terms. Lurking could be equated to reading, interpreting, synthesizing or augmenting for purposes of gaining further acumen, insight and understanding. It shouldn’t be thought of negatively.
But the emphasis and focus is on the direct subject material at hand. What if, for example, I wanted to begin learning about becoming an architect and I were to begin enrolling into online discussion forums of experts and spouting off as if I knew what I was talking about. I’d flame the community, I’d make a mockery of the group and myself, and I certainly wouldn’t be doing myself any good. Wouldn’t a better first step be to in fact lurk around some of the communities, read up on what an architect is or does, get myself a baseline of knowledge for some period of time … and then make the shift into participating and being an active collaborator?

Certainty Principle

An article has come out that states, people who hold false convictions are better at retaining corrected information.  Researchers have used imaging technology to spy on the brain as it corrects strongly held beliefs, shedding light on how might learn from our mistakes.  This is called hypercorrection, say I ask you what 2+2 is and you say 7.  I say how confident are you, you say highly confident.  Then I tell you the answer is 4.  You are more likely to remember it- not just for a few minutes later but weeks and much much longer.

Scientists reason that in hypercorrection, after people discover that ideas they felt very sure about were not inf fact correct, the surprise and embarrassment they feel makes them pay special attention to alternative responses about which they felt less confident.  People then go on to take the corrected information to heart, learning from their errors.

The findings have implications for educational techniques and theory.  The broadest conclusion we might draw from these findings is that we may have the wrong attitude toward errors.  Throughout society and our educational system, there tends to be an attitude that you don't want people making errors and mistakes during learning.  In order to increase effectiveness of long-term learning and understanding, we should structure instruction and training so that likely errors and misconceptions will come up during the learning process, and use them as opportunities for learning.

Here is the link to the article:http://www.scientificamerican.com/article.cfm?id=certainty-principle-people-who-hold-false-convictions-are-better-at-retaining-corrected-information

Human Scatter Graphs

You can either set up an (x,y) chart on the floor or you can select two walls of the rooms to be the axis.  Then you have the students in your class represent the data.  It is a great way to get students out of their seats and have them know individual (x,y) points and be able to understand a graph.  You can set scales for the axis, but the students will stand in position representing a number to travel.

The following website gives examples of activities that the students do on a daily basis.  I would have my students have given examples of graphs that either are made up or come from the book.

This is a great activity to get students engaged and make sure their independent and social learning are at the same level.  Happy Teaching!!

Games

I observed a great teacher the other day and found him letting the students play games, not just one or two... but all of the time.  It is a great way to engage students and have a great rapport with students.  Summit math is just one of these sites.  At Summit Math, we focus on materials that increase understanding and retention of core concepts, using cooperative learning as well as traditional drill and practice.

Summit Math provides different games that can get students engaged.  Here is the site: http://www.summitlearning.com/math/ as I was observing the teacher he had multiple games planned for different days.  He had a Jenga game that had numbers on the blocks that corresponded to different prompts and could use this for different examples.  He had another penguin game where you flip in the penguins to gain points and was very engaging for his students.

Using games in the classroom is a great way to see individual growth and have the students provide social learning for each student.

Assessment II

Different types of presentation and strategies are the reasons why students perform well.  From journals to cooperative learning activities these different assessment strategies are great for students to know that there is more than bubble testing and closed answer solutions (like most assessments are in math).  Some links that are good for thinking outside the box when it comes to assessments are found below.  There are many different and new research based assessments out there and some more information is coming.

http://www.rmcdenver.com/useguide/assessme/definiti.htm

Web 2.0 & Life Long Learners

Given ever-changing societal and professional demands, lifelong learning is recognized as a critical
educational goal. With postsecondary students' increased demand for online learning opportunities and
programs, postsecondary educators face the challenge of preparing students to be lifelong contributing
members of professional communities of practice online and at a distance. The emergence of powerful
Web 2.0 technologies and tools have the potential to support educators' instructional goals and objectives
associated with students' professional preparation and the development of lifelong learning skills and
dispositions. In this chapter, we explain how postsecondary educators can use the Web 2.0 technologies
associated with blogging, social networking, document co-creation, and resource sharing to create
intrinsically motivating learning opportunities that have the potential to help students develop the skills
and dispositions needed to be effective lifelong learners.

For more information you can use the following links that are full of information and research-based strategies that incorporate web 2.0 tools and life-long learners.
http://www.patricklowenthal.com/publications/LLLandWeb20preprint.pdf
http://p2pu.org/en/groups/using-web-20-and-social-media-to-encourage-deeper-learning/content/full-description/

Total Physical Response

Total physical response, also known as TPR is based on the premise that the human brain has a biological program for acquiring any natural concept.  The process is visible when we see how infants recognize words and concepts with pictures and movements.  Using TPR in the classroom is a great way to not only engage your students, but better manage your students in a unique way.

Here is a link of a teacher using total physical response in an algebra classroom using the slope of a line.  http://www.teachertube.com/viewVideo.php?video_id=158801&title=Total_Physical_Response__Slope_of_a_line

On We Are Teachers: there is a total physical response math idea using Xbox 360 and Kinect in the math classroom. http://www.weareteachers.com/teaching-ideas/grant/teaching-idea?app=13149&grantId=50

I hope you use this in your classroom.  Happy Teaching!!