Inspiration

“There are many ways to organize curricula. The challenge, now rarely met, is to avoid those that distort mathematics and turn off students.” - Steen, 2007

            Those individuals who attended NCTM Denver in April 2013 could not have felt anything less than inspired.  Inspired by the energy, enthusiasm, research and knowledge shared by the professionals who swarmed the city.  In the hotels, restaurants, walkways, buses and throughout the convention center, there was a constant hum of those who were energized by the mathematics present at this annual meeting and exposition.

                  In one session, Picture Yourself Having Fun at Math, Mary A. Robertson shared how photography can be used to incorporate real-world situations into the math classroom. The use of pictures can be used to reinforce concepts involving geometric shapes, areas, volumes, similar figures, transformations and so much more. I found myself reflecting on how the simple task of incorporating photography into the math classroom can be used inspire a student to look at mathematics through a different lens (which happened to be one of the hashtags used throughout the week).

Who has heard of mARTh?   The basic idea of mARTh is to connect mathematical concepts in a visual, kinesthetic way to make math fun, hands-on and beautiful. The presenter noted the goal of mARTh is to use creative expression to connect students to mathematical concepts.  This is a teacher whose goal is to help students make a personal, physical and visual connection with mathematics. 

            In another session, Making Cents of CCSS, Doug Tyson and Jason Molesk addressed ways to make inferences and justify conclusions from sample surveys, experiments and observational studies through spinning pennies and simulations.  The presenters shared ways to lead students in a statistical significance test in a way that non-stats teachers can implement…even at the middle school level. Did you know there are pennies from the 1960’s that will land nearly 100% of the time on heads when spun on its side? 

David Masunaga’s Geometry on a Shoestring Budget was described as “the most profound, interactive and dynamic activities that don’t require expensive technologies” and that is exactly what it was.  Masunaga kept the audience captivated and yearning for more with cheap and nontraditional geometric manipulatives that could be used to reason and prove various geometric concepts.  Every person in the room was engaged and inspired by Masunaga; the power of one.

Jo Boaler made a valid and strong point in Using Research to Make a Difference where she clearly noted that producing research knowledge is not enough to make changes in the math classroom.   How do K-8 Teachers Change Their Practices after Learning More Mathematics?  shed light on the aspects of teaching practices connecting a teacher’s knowledge and beliefs which led directly to Ritual:  A Category for Understanding Persistent Practices in Math Education; a theoretical study on the persistence of practices in math classrooms which contributed to a theory of rituals in math education. 

            With so much happening in Denver it is impossible to share every ounce of awe and amazement one experienced throughout the week.  During the opening session, The Power of Just One Teacher, Mayim Bialik shared a mission which all teachers should consider encompassing into their rituals, beliefs, practices and everyday practices: to inspire students to pursue STEM education.  This is not to say that we should expect every student make the maths and sciences the end all of education but as educators we should make it our mission to ignite a spark in every student.  As educators we have the immense and immeasurable power to inspire our students to develop a love for mathematics in some way, shape or form.  Every lesson, activity, assessment and mathematical discussion keep the common core and the mathematical practices in mind.  However, do not forget to inspire, engage and help students to develop an appreciation for mathematics that permeates beyond the classroom; you have the power to make an inspirational difference.

I look forward to another inspirational NCTM conference in New Orleans.

I Can't Do Math!

The dreaded yet famous quote “I can’t do math!” continues to haunt math teachers.  Is this a true statement? Are there students out there who just can’t learn mathematics?

Teachers of mathematics are expected to have a strong hold on mathematical content as a well as the pedagogy needed to support the various learners in the classroom. They have been trained in Bloom Taxonomy, Gardner’s Intelligences, special education and classroom differentiation.  The challenge is designing instruction to bring the learner to a level beyond rote memorization and regurgitation to a level of inquiry and conceptual understanding. This requires the teacher of mathematics to consider the way in which a student’s mind is activated.

Based on How the BrainLearns Mathematics by David A. Sousa (2008) there are several areas to consider. 

·      Make math meaningful.  If a teacher cannot answer the question, “When am I ever going to use this?” in a way which is meaningful to the students, then the teacher should consider why the concept is being taught. Learning is stored in long term memory when it has meaning. Teachers who find themselves frustrated with a classroom that cannot remember a process from one day to the next are teachers who should focus on establishing meaning for students.

·       Make math emotional. Middle school students are emotional beings.  They are quick to share their opinions and feel strongly in what they believe. A good teacher uses this to his/her advantage.  Take a common objective for the day and make it exciting.  Sparking interest and emotion is yet another way into the long term memory area of the complex brain of a middle level student; good teachers know this and use it to their advantage.  

·       Timing is everything.  The first ten minutes of class, after student attention has been gained, is a peak time for learning.  The good teacher uses these ten minutes to teach new material knowing the brain is absorbing all the information being presented.  Good teaching during these ten minutes of prime learning time is a preventative to “I don’t remember what we did yesterday.”

·       Use downtime to practice. After the first ten minutes of processing information the brain reaches it potential and starts on a downward trend for retention.  The brain is essentially a sponge which cannot hold any more. A good teacher gives students time to utilize and process the new mathematics after peak learning.  This utilization and processing period is the brains way of storing information into the long term memory bank; exactly what teachers wish for.

·       Closure is a mathematical seal.  Given a processing break, the brain begins to rejuvenate.  Spending the last 20 minutes of class to bring closure to a lesson is another good use of student learning.  A good teacher knows this is the last chance to make a meaningful connection to seal the mathematical objectives.  Stress the key aspects of the class and make the last ten minutes the grand finale.

·       Ten is a magical number.  The working memory of a middle level student works best in ten minute chunks.  After ten minutes of the same activity or instructional mode, the mind of the middle school student veers off.  Boredom, daydreaming and distractibility all set in.  A good math teacher knows to change up the activity, instruction and mode of instruction. This is the time to use Blooms and Gardner.

·       Make room for high level mathematics. The brain recognizes and stores patterns; patterns of processes, skills and knowledge.  Teachers at all levels have techniques to the speed of pattern recognition; flash cards, tips to break down word problems, acronyms, rhymes, songs, etc.  These techniques support the brain in long term memory storage; making room for deductive reasoning and high level mathematics.  A good math teacher develops lessons which go beyond the rote performance of skills and knowledge, knowing the brain is well prepared for mathematical reasoning and deduction.

Everyone has a brain.  Everyone can do math.  The key is fine tuning the methods in which mathematics is presented; methods which maximize learning for all minds and eliminate those who believe “I can’t do math!”

Stop Giving the Answers

This group of seventh graders is quickly learning that there are very few answers given in class.  Ask a question and you get a question back.  Ask if your answer is correct and you will be asked the same question.  Have a different answer than your classmates?  Be prepared to share. 

Sharing the correct answers requires little thinking.  In the typical classroom, a teacher may stand in front of the class and read the correct answers to students or even ask students to share their correct answers.  Students correct their work by marking answers right or wrong and then ask for clarification on specific problems.  Additional students may then be asked to present the correct process or at least a process, which works for the given situation.  Take a few minutes to reflect on the level of mathematical discussion and thinking, which occurs when this process of sharing the correct answers is used.  Are students thinking? Are they learning?

Instead of giving the correct answers, peruse the classroom and look for students who have the incorrect answers. Yes, the incorrect answers.  Ask these students to share their work, processes, understanding and reasoning with the class.  Now, facilitate a discussion.  Look at the thinking used by the students.  Ask students to explain their thinking.  Ask students to look for errors in thought processes or calculations.  Can they explain why this process did not work? Can students direct their peers to think of the process in a different manner?  Was the individual on the right track but needed guidance for the next steps?  Take some time to reflect on this process.  Are students thinking?  Are they learning?

Force discussions and thought in the classroom by pushing students out of their comfort zones.  Allow them to come into class without answers.  Start accepting incomplete processes with questions as to where to go next.  Lets be clear.  Blanks and question marks are not okay.  Students must show some attempts and comments as to where they were hitting a roadblock.  And if the other extreme occur where students are getting all the answers correct then they are not being challenging.  Give students work that requires them to think beyond the rote skills and the skill range where they will earn 100%.  Force students to challenge their mathematical thinking. This is where the mathematical discussion and learning will occur.

Assign tasks and activities which have different interpretations and perspectives.  As students ask questions, require the class to come to a consensus.  In other words, when students ask what a requirement means let the class to determine the answer.  Don’t give students your perspective or interpretation.  Allow students to think about the mathematical context and discuss the best ways to approach the situation.  Let students discuss their perspectives and reasoning.  Is there just one?  Is there only one right answer?

According to the Common Core State Standards Initiative (2012), mathematically proficient students make sense of problems and persevere in solving them.  They look for entry points to solutions, make conjectures and develop a plan towards a solution.  The Common Core State Standards Initiative (2012), describes mathematically proficient students as those who can listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. This can happen when students are challenged beyond the provision of the right answers.

Challenge your students to think.  Develop the mathematically proficient student.  Stop giving the answers and instead give students the gift of learning.

           

Implementing the Common Core State Standards. (2012). Common Core State Standards Initiative. Retrieved October 30, 2013 from http://www.corestandards.org

Mathematical Share-a-thon

Wouldn’t it be nice if you opened your email and up popped a series of mathematical supports?

Let’s start the year off right. Below I have listed ten resources that I think every math teacher should be exposed to. Add them to your math toolbox and enjoy. Your task is to continue this share-a-thon. Take the time to write a quick email listing your ten mathematical resources and send it out to as many math teachers as you can (the more the merrier). Ask these teachers to then do the same. A little exponential growth would be a good thing.

Be creative and don’t worry if your resources are not web based, books are a good thing too! Can’t think of ten? That’s okay. The idea of this mathematical share-a-thon is to support one another in this sometimes lonely field of teaching. Let’s share the wealth we have stored in our file cabinets and join together to spread the joy of mathematics.

Katrina’s Ten Mathematical Resources

1. Mathalicious contains CCSS lessons which ask real questions in open-ended ways requiring students to problem solve and think critically.

2. Yummy Math provides teachers with real-life lessons to bring into their math classrooms. Concepts are explored that are interesting to students with the goal of increasing mathematical engagement, reasoning, critical thinking and communication.

3. Livebinders is a bookmarking tool with resources galore. Create and organize your own materials. Search through other professional binders to find math content sorted by tabs. All the research is done for you here. You just have to do a quick search. Try searching for “CCSS” and you will be amazed what comes up!

4. TeachersPayTeachers is open marketplace where teachers buy, sell and share teacher created resources. Creating an account is free and you can download resources for as low as $1.

5. Formulator Tarsia is a free software download. With Tarsia you can create mathematical learning activities (jigsaws, domino activities, card sorting activities, etc) to print out, save and exchange for classroom use.

6. NRICH is an online resource which offers free enrichment materials to help inspire and engage learners.

7. Pinterest is the latest crave in visual bookmarking. The teacher resources to be shared are too vast to name. Take the time to investigate this tool and you will truly be amazed at the resources readily available to you. Follow my Pinterest boards www.pinterest.com/theboss1000/ and I will follow you back. You can even collaborate with a colleague, like Lynn Dizazzo and I have....check our our boards http://www.pinterest.com/pendesk/

8. Teaching Channel is rich with mathematical videos, lessons and general teaching resources. This collection is a phenomenal showcase of effective teacher videos to inspire teacher learning and instruction. Check out the new videos related to the CCSS!

9.  Ole Miss Math Contest adds some worldwide competition to the classroom. Students use various mathematical skills to work through the challenge of the week for some friendly math competition. If they are lucky, they may even win an Ole Miss Rebels t-shirt.

10. 101 Questions is Dan Meyer’s latest mathematical creation. Dan posts photos and then poses his big question, “What’s the first question that comes to mind?” Great hooks for lesson starters.

Don’t forget to share your ten!

Even better share them on Twitter....I can be found @mrskatrinahall and @pendeskllc

Sharing a Light on PLNs

Reading through several Tweets and blogs I fell upon a fun way to connect with professionals, extend our PLNs and an opportunity to continue with the blogging challenge for 2014.  

According to the Dyslexic Professor @mbfxc, what started as the Sunshine Award (not sure what this award really is or was) has now become an opportunity for bloggers to share a little about themselves and learn about other members of the blogging community. 

So here are the rules...

• Acknowledge the nominating blogger (I was not nominate but inspired by @mbfxc)
• Share 11 random facts about yourself
• Answer the 11 questions the nominating blogger has created for you
• List 11 bloggers. They should be bloggers you believe deserve a little recognition and a little blogging love!
• Post 11 questions for the bloggers you nominate to answer and let all the bloggers know they’ve been nominated. (You cannot nominate the blogger who nominated you.)

11 Random Facts About Me...

1. I am not a morning person (which is odd since I wake up very early) and prefer to be more active at night.
2. My major in college was computer science but I decided to change (with only 2 classes left) to change to secondary education in mathematics.  Wish my advisor told me to stay finish the two classes and then continue with a teacher certification after.
3. I love great white sharks.  I do not scuba dive so going into a shark cage is not an option but I would like to see airjaws off the coast of Australia some day.
4. Summer is my absolute favorite time of year.  I couldn't live without it.
5. If I had not married and had children, I would be living on a tropical island.
6. I have had several pets in my life....fish, birds, rabbits, hamsters, dogs, cats and more  No large animals and no serpents of any kind.
7. Buying a new handbag makes me very happy:)
8. I have been a student for the majority of my life.  Starting from preschool right through  today as a doctoral student.  
9. I have been tracking the weather for some time to determine the best place to retire....California is out.
10. My Boston Terrier is a calming factor for me.  Whenever I have a bad day, playing with him helps me to de-stress and focus on the good things in life.
11. There are teachers who I have worked with in the past and work with now, who inspire me me everyday.  Thank you! 

Answers to the Questions from the Bloggers Who Nominated Me
Since I was not nominated I am just going to answer the questions which the Dyslexic Professor answered.

• Why did you start blogging? I find myself learning so much from other bloggers and feel as if it truly is a great way to share lesson, ideas, thoughts and reflections.   

• If you could possess only one piece of hardware, what would it be? I would surely keep my iPad.  This would let me stay involved in so many ways...social media, learning, friendships, etc.

• What was your favorite lesson to teach in the classroom? I love the unit on exponential growth which I extend into a project where students make a difference in the world.

• If education wasn't an option in any form, what would you be instead?  If I had to work  then I would venture into owning a small restaurant.  If I did not have to choose a "career" then I would be a beach reader for sure.  The beach and books are the best for me.

• What was the title of the last book you read for fun? And the Mountains Echoed by Khaled Hosseini

• What was the hardest lesson you learned? That mistakes are a mandatory process for true learning to occur.

• What is your favorite movie of all time? Charlie and the Chocolate Factory and the Wizard of Oz

• What's your proudest moment? My proudest moments (I have three) is having all three of my children.  Nothing can beat these moments.

• Have you ever cried at a YouTube video? No....This sounds insensitive but I guess I have not seen the "right" videos.

• How do you explain your job to people?  My job is like a circus where I appear to be the ringmaster but the students are the true focus.  It is my job to guide them to show their talents and strengthen their recognition.

• What's the biggest prize/money you've ever won? Hmmmm.....I rarely win raffles or prizes but I did win a football pool a fews ago which was pretty funny since football is the only sport I do not enjoy watching.....sorry :(

11 Bloggers I Want to Know More About...

A few who I hope will start blogging...

1. Steve Capraro @mrcapraro 
2. Lynn Dizazzo @mrsdizazzo 
3. Amy Bouchard @msamybouchard
4. Susan Connelly @connellysue
5. Laura DeRose @hypatiahistory
6. Karen Coutu @karencoutu

Bloggers who challenge me as a learner and I want to know more about...

1. Julie Reulbach @jreulbach
2. Cathy Yenca @mathcathy
3. Mary Dooms @mary_dooms
4. Robin Nehila @Radical_Robin
5. Colin Graham @ColinTGraham
6. Denise Gaskins @letsplaymath
7. Leslie Nielson @InnovativeEdu
8. Patricia Hensley @loonyhiker 
9. Angela Maiers, @AngelaMaiers
10. Sandy Kinell @EdTechSandyK
11. Jacqui Murray @askateacher
12. YOU! (If you haven't been tagged yet, don't let that stop you! Write a similar post and tag some folks. Be sure to Tweet me and let me know you did it, or leave a comment below!)

11 Questions For the Bloggers I Want to Know More About...

• What made you venture in to the arena of education?
• What has been your greatest failure from which you learned the most?
• How would you transform education?
• What is one item from your bucket list that you have yet to complete?
• What is the best advise you would share with a new teacher?
• If you change one thing in your life, what would it be and why?
• If you could meet any individual in the world, who would that be and why?  (past or present)
• What aspect of education keeps you in this field?
• What is the most inspiring book you have read?
• What is one word you would use to describe yourself?
• What inspires you?

All original work in this post by Sandy Kendell is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.