Solving Word Problems

Learning Strategies- Math Strategies for Solving Word Problems

General Tips
Learning how to solve problems in mathematics is knowing what to look for.  Math problems often require established procedures and knowing what and when to apply them.  To identify procedures, you have to be familiar with the problem situation and be able to collect the appropriate information, identify a strategy or strategies and use the strategy appropriately.

4 General Tips are: look for clues, have a game plan, use strategies to solve the problem, reflect on the answer.

Other strategies include:
STAR Strategy
RIDGES Strategy

Click the link below for more information and strategies: http://www.beltonschools.org/_layouts/BSDDOcuments/SPED/stratograms/Math%20Strategies%20Word%20Problems.pdf

Educational Hashtags

http://www.cybraryman.com/edhashtags.html
http://edudemic.com/2011/10/twitter-hashtag-dictionary/
http://edudemic.com/2012/01/20-hashtags/

Featured above are three great sites for twitter hash tags that contribute to education.  If your on Twitter then you know the common hastags, but my favorite is #mathchat.  You can get high quality lesson ideas or interactives you can use in any math classroom specific to you.

Goodreads

Most educators (hopefully) know what Goodreads is and how you can use it in your classroom.  I think I have a previous blog post about that..... hmmm.  But I digress, I feature "Do Good with Goodreads" this helps others experience the joy of curling up with a good book.  Each month Goodreads highlights a different charitable foundation that promotes education and literacy.

One of my favorites is Milk+Bookies, the event-based nonprofit aims to teach young ones about dual causes: literacy and philanthropy.  The organization hosts events for kids- complete with story time, music, and milk and cookies- and asks the children to select books to donate to kids in need.  For parents and teachers interested in hosting their own events Milk+Bookies also offers resources for book-themed parties, class projects, and school book fairs.  The charity has donated more than 21,000 books and encouraged over 4,000 children to experience the joy of giving.

http://www.milkandbookies.org/
http://www.goodreads.com/book_news_posts/58-milk-bookies
http://www.goodreads.com/featured_lists/5-do-good-with-goodreads

Incorporating math as a way of reaching students through books fiction or non-fiction is a great way to get students interested in mathematics.


 

Skype in the classroom

Skype is a free application that allows you to call people from all over the world using the Internet.  When you contact another person that uses Skype you talk or chat for free.  Best of all you can tell when another user is online and what their status is so you know if they are available.

Increasingly, educators globally are transforming their classroom using Skype to create powerful, authentic, motivating learning experiences for their students.  From connecting with classrooms in other locations to learning about each others’ culture to connecting with content experts – educators are extending learning beyond classroom walls.


It’s also worth keeping parents and families informed of why and how you’re using Skype in the classroom so they feel comfortable with the process.

http://theedublogger.com/2011/04/03/the-complete-educators-guide-to-using-skype-effectively-in-the-classroom/

Questioning Strategies

Listed below are research-based questioning strategies you can use in your classroom.  These meta-cognitive questions can help students at each stage of the problem-solving process.  As students work on problems that require problem solving, remind them to ask themselves these questions.

Understand-  See

• How can you say the problem using your own words?
• What more do you need to know?
• Could you draw a picture to show the problem?
• Have you solved a problem like this before?

Plan- Think

• Have you solved a problem like this before?
• What do you guess the answer might be?
• What plan will help you find an answer?
• What materials or tools do you need?
• How can you make this simpler?
• What kind of picture would help you?
• What patterns do you see that would help you?

Work- Do

• Is your plan working?
• How do you know?
• How could you explain what you did?
• How close to the answer was your guess?

Check

• Does your answer make sense?
• How could you solve this problem another way?
• Could you make another problem like this one?
• How close was the answer to your guess?

Print out: http://cesa5mathscience.wikispaces.com/file/view/K-2+Math+Research-Based+Questioning+Strategies.pdf

Google Cloud

I started typing this blog post about Learning in the Google Cloud it is an application on Google Chrome where you can discover new educational concepts and exciting ways to use products and services from Google.  The thing is the site is poorly constructed and its "new educational concepts" are outdated.

The site is not regularly updated (almost not at all).  But as I was typing this is what I was saying and you can decide.

The different Google applications they have engaging lessons, self-paced learning, your school in the cloud, informational accessibility.  It doesn't give any lesson ideas just places where you can see more information about the different topics. The one good thing it does is give information of Google's different applications and tools you can use in your classroom. http://google4learning.comule.com/create.html

http://google4learning.comule.com/index.html

Digital Differentiation

Technology is a tool that can be used to help teachers facilitate learning experiences that address the diverse learning needs of all students and help them develop 21st Century Skills.

Student-driven learning experiences should be driven by standards-based essential questions.  These questions should be open-ended to allow for flexible learning paths.  Devise questions by looking at the standards that determine what  we teach.

Flexible learning paths: use digital tools to provide students with flexible learning paths to meet their unique learning styles.  Click the link below if you want more information.

Teacher facilitated learning experiences: the role of teacher shifts to facilitate student-driven learning experiences.  This new role allows teachers to maximize instructional time because of the classroom structure provide opportunities for frequent interaction with individual students for assessment, modification, reteaching, and enrichment.

http://d97cooltools.blogspot.com/2012/02/digital-differentiation-get-wired.html

Google Apps

Enhance classroom learning whether you need student tools, teaching aids, or administrator utilities, the Apps Marketplace helps you discover, purchase, and deploy web apps that integrate with Google applications for Education.

The marketplace includes dedicated education professionals from 3rd party vendors, many integrations synchronize with Google Calendar and documents.  Teachers can manage a single directory of both users and applications from the same unified interface, reducing overhead and improving security.

More than 12 million students and teachers are using Google Apps (why aren't you?)

http://www.google.com/apps/intl/en/edu/index.html

Cell Phones II

I was thinking of incorporating cell phones in to the math classroom and was getting materials from the library when I found an interesting book called Cell Phones in the Classroom by Liz Kolb.

There are a few lesson plans in the book that relate cell phones and mathematics, but nothing that is a stroke of brilliance.  The lesson covers students using their cell phones to take pictures and use voice mail to record where they use algebra in everyday life.

Some better information I can give you is web 2.0 tools that you can use to ease your way in to cell phone use in your classroom.  Here is a list of some of the web 2.0 tools featured in the book:

• www.dialmycalls.com
• www.cinchcast.com
• www.geograffiti.com
• www.historyphone.net
• www.phonevite.com
• http://core.rminder.com
• www.rondee.com
• www.mymemorizer.com
• http://notify.me
• http://pulse.to
• http://remind101.com
• www.schoohoo.com
• www.schooltipline.com/en
• http://studyboost.com
• http://swaggle.mobi
• www.wetext.com
• http://wiggio.com
• http://zxing.appspot.com
• http://jumbli.tv
• www.letsgovote.com
• www.smspoll.com
• www.textthemob.com
• www.cellblock.com
• http://flixwagon.com
• http://www.livecast.com
• www.tumblr.com
• www.zannel.com
• www.beema.com
• http://mobilestudy.org
• http://mobiode.com

Passion Based Learning

There are some key points that address the issues around passion-based learning that came from the book A New Culture of Learning: Cultivating the Imagination for a World of Constant Change by John Seely Brown.

Reach out to the disenfranchised: most teachers like the creative, passion-driven student passionate teaching reaches out to the students who normally are not engaged in the classroom.

Show relevance to life outside the school: this is not about matching students with topics that interest them, it's about presenting subjects to students in a way that is relevant.

Indoctrinate passion into the system: rub off your passion to other teachers and administrators, walk in the school everyday ready to go, knowing that all of your lessons are the greatest (even if you made them last night.)

Try using the schoolwide enrichment model: this model identifies student strengths, nutures skills, and creates authentic opportunities for students to utilize these skills not just as students, but practicing professionals.

Digital media is the key: passion involves an extreme performance with a deep questioning disposition.

Tap into the wisdom of your trusted peers: teachers need to publish their innovative work and share it with their personal learning networks.

Become digital citizens: guide students.  Having teachers and students learn side-by-side can provide great opportunities for building respect and openness.

Passion is infectious:  being around passionate people is the best way to become passionate. Simply said.

Connect with Parents: every teacher knows that building relationships with parents is crucial.  By identifying the strengths and talents of parents, parents gain a sense of recognition and human value and feel engaged in their students learning.

Follow the link if you would like to read more: http://mindshift.kqed.org/2011/07/nine-tenets-of-passion-based-learning/

http://www.21stcenturycollaborative.com/2011/04/interview-passion-based-learning-for-the-21st-century/

GoCognitive

GoCognitive supplies free educational tools for neurscience.  It allows free access to materials for students, educators, and researchers in cognitive psychology and cognitive neuroscience.  GoCognitive supplies interviews from field innovators it spans upon cognitive psychology, working memory, attention, neuroscience, cognitive neuroscience, language processing, linguistics, synesthesia, mirror neurons, and brain categories.

GoCognitive also applies demos that you can filter by tags to visual pathways to selective attention, working memory capacity to implicit memory tests.  This can help any teacher find the best possible ways for their students to lean.  Links are below.

http://gocognitive.net/

Lominoes

I am not going to go in to the details of lominoes, because they are increasingly complex as I read the pdf, so the pdf is posted below.  Lominoes would be a great addition to any math classroom.  Lominoes can include any of the following topics and give your students a visualizing way to describe complex math problems.  Lominoes can be used in any of the following:

• 2D puzzles
• 3D puzzles
• Tetrons
• Complex Fences
• Complex Buildings

http://schoenpuzzles.com/webbooklet.pdf

This would be a great way for Math Club participants to gain a higher mathematical thinking about space and shapes, and how those shapes fit in a certain shape.

Pulse Project

Pulse Project is podcasting, university lectures, and science education.  The website boasts that it has something for everyone.  Pulse Project has a wide range of freely accessible audio and video lectues on the sciences and medial humantities for both general and specialized audiences.  Aiming to reflect and inform debates amongst academics, students, and the wider public alike.  Pulse aspires to facilitate a broader engagement with the formative scientific and historiographic questions of our time.

http://www.pulse-project.org/front

The website has been updated and now includes weekly podcasts, conferences, videos and lectures, expert explainations, and scientific images.  All of the material which some relates to math gives great in depth talks on math about how girls are as good as math as boys, graph theory, and model students.

http://pulse-project.org/node/411 this link provides a link directly to the talk that I listened to about how tough Pac-Man is to play and understand, as well as how girls learn math better than boys.

3D Graph Equations

From calculus finding level curves in certain 3D shapes is a great resource for visually finding answers.  Using this will help students visualize calculus.  Warning this does involve time and I normally give it as an extra credit assignment for students since it involves a serious amount of time.

It involves a graphing calculator to find the certain curves at different intervals, but looks amazing.  I have thought about making a few for examples.  Possibly easier ones that just involve planes so the students can grasp the concepts more easily, since the hardest part about Calculus is "seeing" what three dimensional shapes look like.

Hope you use this in your classroom.

http://math-fail.com/2012/01/taking-math-to-a-whole-new-level.html

Minesweeper

I have come across an article of one of my favorite authors Ian Stewart and he was analyzing a simple computer game most nerds (like me) play constantly minesweeper.  The solution he came up with involves locating hidden mines on a grid by making guesses about where they are located and using clues provided by the computer.

The actual article length is pretty lengthy, so I am going to try to sum it up in about a paragraph.  He was trying to initialize the mines using probabilities famous theorem stating P=NP and realizes that it may not be as simple as that and tries to prove that the problem is non-P, Stewart goes through many different proofs and realizes that it is really a hard problem to solve and ponders on the thoughts that such a simple game can have "intractable consequences, but mathematical games are like that."

Here is a quote that sums up the end, "If you're interested in those million-dollar prizes, a word of warning. The Clay Institute imposes strict rules before it will accept a solution as being valid. In particular, it must be published by a major refereed journal, and it must have been 'generally accepted' by the mathematical community within two years of publication. But even if you're not going to tackle anything as daunting as that, you can have a lot of fun playing Minesweeper, secure in the knowledge that it encompasses one of the great unsolved problems of our age."

Mind Shift

The site http://mindshift.kqed.org/ answers the questions how we will learn in the future.  They have 4 main topics that they post on each day: culture, tech tools, research, and learning methods.

Culture: how trends in technology such as social networks, internet privacy, cyberbulling- influence education.  It's main articles are directly related to educational hot topics.  Such as what does your school know about you, parent and students learning together, extra-curricular learning centers, and creating a better tomorrow for your community.

Tech tools: the newest devices, software, sites, and apps that are changing the way we learn.  Gives insightful tools for teachers on using technology in the classroom, websites for lesson ideas and web 2.0 tools, and creating your own textbook.

Research: the latest findings from experts in the field related to the future of learning.  Gives students and teachers tools on how to learn smarter, how trustworthy is research, and how to be more search savvy.

Lastly learning methods: innovative ideas- projects, processes, curricula, and more- that are transforming how we teach and learn.  Gives teachers new ways to think about how their students learn, educational applications, and other great technological ideas you can use in your classroom.

They Don't Teach You this in School

All the videos on the website http://theydontteachyouthisinschool.com/ are of the individuals answering the question: "What's one thing that they didn't teach you in school that you wish you had known when you were younger.  The articles are written by many different people, on a huge range of topics.  If something interests you, chances are that it will interest other people as well.  Get involved and make a contribution.

http://theydontteachyouthisinschool.com/get-involved/

Sometimes teachers don't have enough time to help students become the most successful they can possibly be.  This site contains both videos and articles to learn the right stuff and learn important lessons in a minute or less.

Math Classroom Activities

Attached below is a link to different math classroom activities ranging from Jump Rope Math, Hula Hoop math, different problem sheets, cost comparisons, and factoring activities.  These activities were created with one goal in mind and that was to incorporate physical movement and activities in to the math classroom.

http://www.clocc.net/partners/group/school/MathActivities.pdf

These activities are made for many different age levels and ability levels, but I know that you are talented teachers and just a little idea and your imagination can be a great tool for your student's success.

Happy Teaching.

Expeditionary Learning

Expeditionary learning inspires and motivates to learn, engage teachers, and students in new levels of focus and effort, and transform schools into places where students and adults become leaders of their own learning.  This site provides a model that challenges students even those starting with low skill levels with high-level tasks and active roles in the classroom.  This model succeeds in urban, rural, and suburban schools and at every grade level.

At this site there are places for professional development, recommended reading, evidence of the model working, quality of student work and academic achievement.

http://elschools.org/

Real World Math

http://realworldmath.org/Real_World_Math/Lessons.html

This place is for lessons that use Google Earth to present math topics in unique ways.  They explain different types of concepts and measurement.  There is a place for project- based learning activities that will include lessons that will require the collaborative efforts of students in pairs or groups.  These lessons may be a longer duration and require outsourced material.

There is also a place for students to explore lesson that will follow non-traditional math topics such as fractals, topology, or modern geometry.  This includes space lessons that will utilize Google's Moon, Mars and Sky for activities in math and other subject areas.

Modular Robotics

Cubelets are magnetic blocks that can be snapped together to make an endless variety of robots with no programming and no wires.  You can build robots that drive around on a tabletop, respond to light, sound, and temperature, and have suprinsingly lifelike behavior.  Each cubelet cube in the kit has different equipment on board and a different default behavior.

http://www.modrobotics.com/

Gold Rush Math

Looking for a supplemental activity to round out your lesson plan about the Klondike Gold Rush?  The following activities were designed by instructors for instructors limited by time and resources.

The activities appeal to a wide range of learning styles and meet many learning requirements.  These activities make use of writing skills, reading, math, art, and physical education.  Although arranged in a chronological order for following the gold rush story, individual activities can act as a stand alone components.

http://www.nps.gov/klse/forteachers/curriculumactivities.htm
http://www.nps.gov/klse/forteachers/otherresources.htm

Google+

This post is to present information to students, faculty, and administration about how to maximize the use of Google+ for learning and connecting at your organization.

Google+ allows you to organize your contacts according to circles, video conference at google hangout, share google documents with others, have conversations with one another with stream, search within google plus.

You can share information with specific circles, gather questions with surveys with google, hold office hours with video conferencing (or with parents!!!), distance learning, review video with students to teach difficult concepts, have collaboritive writing with your students or collegues.

This is an easy way for students be engaged in school while they are out of school, meet classmates face to face before class even starts, share ideas with fellow teachers.

Start using Google+ in your classroom and school.

• To create an account visit: www.google.com/+    

• To create a Google+ page for an organization visit: www.plus.google.com/pages/create   

• To learn more about Google+ for the university community, visit: www.google.com/+/learnmore/universities

• For help, visit Google+ Support at: www.google.com/support/plus

PBiS

PBiS stands for positive behavioral interventions and support for effective schoolwide interventions.

One of the foremost advances in school-wide discipline is the emphasis on school-wide systems of support that include proactive strategies for defining, teaching, and supporting appropriate student behaviors to create positive school environments. Instead of using a piecemeal approach of individual behavioral management plans, a continuum of positive behavior support for all students within a school is implemented in areas including the classroom and non-classroom settings (such as hallways, buses, and restrooms). 


Positive behavior support is an application of a behaviorally-based systems approach to enhance the capacity of schools, families, and communities to design effective environments that improve the link between research-validated practices and the environments in which teaching and learning occurs. Attention is focused on creating and sustaining primary (school-wide), secondary (classroom), and tertiary (individual) systems of support that improve lifestyle results (personal, health, social, family, work, recreation) for all children and youth by making targeted behaviors less effective, efficient, and relevant, and desired behavior more functional.

http://service.columbia.k12.mo.us/pbs/pbis-lesson-plans/
http://www.pbismaryland.org/schoolexamples.htm
http://www.pbis.org/

Incentives

Prizes and punishments are part of controversial topics for teachers and many teachers see extrinsic material rewards as an appropriate and effective way to manage behavior in the elementary classroom.  Other teachers don't want to bribe their students to do work that they should be intrinsically motivated to do on their own.

In my classroom if a student does something well or I see that they should be rewarded for something I normally give the students a homework pass to use on a missed assignment or an assignment they forgot to turn in and this seems to motivate students to get a homework pass and keep it fair for students who don't get one.  If homework passes aren't used and saved till the end of the semester they can use it on their final for 5 extra points.

Other incentives that I use in the classroom are educational computer games that I put on the smartboard if they finish their assignment they can play a game till the end of the period.  If you have any suggestions or incentives that work in your classroom please post below.

Happy teaching!

Pedagogy Badges

From connected learning, pedagogy badges (thinking about how we teach).  These will address what outcomes we want our students to come away with and what experiences we want our students to have.  Pedagogy badges allow teachers to codify our teaching and learning experiences.

Featured below is a Youtube video that presents all the information and kind of how it works.

Short Story Math

Going off yesterdays post, if you are not comfortable using iPads in the classroom, or your school does not offer iPads in the classroom. You can still use historical math events in your classroom.

Have your students use real math history and create historical fiction mini-books where their creativity and imagination can grow.  Other science-fiction writers have done this and they have become wildly popular with science fiction fans.  Logicomix is a great example and use it as template for the students to write or draw for a historical perspective.

http://kasmana.people.cofc.edu/MATHFICT/search.php?orderby=title&go=yes&medium=ss
http://home.earthlink.net/~mathprose/index.htm
http://www.helium.com/knowledge/123682-short-stories-a-math-mystery

History of Math Comics

Comic Book is a application on the iPad where you can take pictures or use pictures off the web to to put them together.  A certain lesson can come from gathering different images and having your students put together a collage of different math historical events.  Students from different levels can feel engaged in mathematics and get a sense of feeling apart of math.

Creating a rubric where students incorporate math they are learning and the history behind is a great way of incorporating both while using the students creativity.

Using comics to teach concepts: http://krambecktechtips.blogspot.com/2012/01/using-comics-to-teach-concepts.html

Hands Down

Some of my students have been excited about a review game that I played when I was in school.  Hands down is one way that all of my students can get engaged in the math classroom.  I normally supplement Hands Down with jeopardy on the smartboard.

Smartboard has a notebook file that is free to download on their website, some jeopardy files are better and some are not as great.

I normally have all the students participate and have them in groups, where they have to turn in the assignment after we finish.  I give out homework passes for students who win, but this turns out to normally be the same students, so I have begun to assign groups.

Good luck, Happy Teaching!!

GradeCam

If you give tests using Scantron, you should give GradeCam a try.  Set up a test and enter the information for the test, the student will print off a copy of the answers hold up the completed form and scan it in with student view. It will automatically give the students and your gradebook the score.  It will give the students in a spread-sheet type format with the name, score, and percentage.  The formatting allows for item analysis and analysis by student.

Give it a try in your classroom.

Happy Teaching!
http://interlockedpieces.com/?p=1387

Codes in Class

Codes have been around for hundreds of centuries.  I am currently reading The Code Book by Simon Singh and it paints an amazing portrayal of how we use codes now everyday when we go on the internet to phone calls, to making sure the https: is really secure.

Using simple code manipulation any student from 8th grade can accomplish this.  At a particular school in Nebraska they use codes to cover WWII material and I thought this would be a great material for all schools.

Most people who major in math or education with a background in math, have to take a class called Number Theory which is the major component of modern codes, I happen to be taught by one of the contributors to the field of Number Theory and found the course stimulating along with applicational.

At the end of The Code book is examples for the reader to do, this one is a Caesar Shift Cipher, see if you can figure this one out?

MHILY   LZA   ZBHL   XBPZXBL
MVYABUHL   HWWPBZ   JSHBKPBZ
JHLJBZ   KPJABT HYJHUBT   LZA
ULBAYVU.

Math Circles

Math circles are a form of education enrichment and outreach that bring mathematicians and mathematical scientists into direct contact with pre-college students.  These students, and sometimes their teachers, meet with mathematical professionals in an informal setting, after school or on weekends, to work on interesting problems or topics in mathematics.  The goal is to get the students excited about mathematics, giving them a setting that encourages them to become better mathematicians.

"What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises." -G.C. Lichtenburg



More information about math circles can be found below:
http://www.mathcircles.org/
http://www.themathcircle.org/
http://mathcircle.berkeley.edu/