Math tends to get a bad reputation.  Let’s make sure we teach it the best possible way and change that!  We need to be teaching math with DIFFERENT approaches than we use for other subject areas.  Check out these math-specific insights to see how to approach math education.
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Neuroscience Behind Math Learning
 
An article from the National Center of Biotechnology information shares some important findings and insights regarding the brain and math learning.  The purpose of this opinion paper is to make a case for neuroscience methodology as a modern tool contributing to the debate on how mathematics should specifically be taught to students.
 
In their studies, neuroimaging provides a lot of insight into which parts of the brain are working during specific mathematics tasks.  One MRI study of mental arithmetic has shown that the pattern of brain activation changes with student age. 

​Basically, the functional maturation determines the amount of connectivity in a student’s brain that would improve solving mathematical tasks.

Mathematical Learning Is At Its Peak...
 
… When Students Develop a Mindset for Math
 
To successfully learn math, students need to develop the correct mindset.  Better Explained provides an insightful guide on why and how to develop a mindset for math.
 
The author provides thoughtful statements and explanations to develop the right mindset, such as “Factual knowledge is not understanding; be open and creative; realize that you can learn.”
 
"Growth mindset" has been on the radar of most educators for a few years now.  It's popular and important.  But I had not been aware before just how critical it is to mastering concepts in math class.  This re-inspires me to explicitly teach growth mindset and encourage it on a more consistent basis.

This article makes you take a step back and reconsider how we approach thinking about learning math.  Are we prioritizing this enough??
 
 
… When Math Provides Joy
 
According to an article from Stanford.edu, there is research that reveals the best way to learn math is through pleasant experiences.  Can we replace some tedious lessons with some more joyful ones?
 
Professor Jo Boaler states, “Students learn math best when they approach the subject as something they enjoy.  Speed pressure, timed testing and blind memorization pose high hurdles in the pursuit of math.’
 
Fortunately, the new Common Core Standards deemphasize rote memorization of math facts.  Although knowing these facts are important, it’s more important for students to learn the facts through developing an understanding.
 
Memorization, speed, and test pressure can be damaging and lead to math anxiety, which, as you might guess, is not a step in the right direction for math learning!

 
… When Students are able to Grasp Number Sense
 
An article, Fluency without Fear” by Professor Jo Boaler, the same graduate professor as quoted above, writes about how critical number sense and fluency are to teaching mathematics. 
 
Research tells us that students understand more complex functions when they have number sense and deep understanding of numerical principles, not when they blindly memorize facts to quickly recall.
 
Boaler worked with PISA analysts at OECD and studied data data from 13 million 15-year olds across the world.  It showed that the lowest achieving students are those who focus on memorization and who believe that memorizing is important when studying for mathematics.  “This idea starts early in classrooms and is one we need to eradicate. The highest achievers in the world are those who focus on big ideas in mathematics, and connections between ideas. Students develop a connected view of mathematics when they work on mathematics conceptually and blind memorization is replaced by sense making.”

Concepts and connections are more vital to math sucess than memorization.
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It turns out that basic number sense is a huge key to success in math.  The basic brain connections from early stages must be in place before students can advance to the next level.

Then, as students progress through their developmental stages, they can process new levels of math in new ways.  Student brains light up differently at each age, because the mental connections build and grow.  They can process new levels of math learning as they learn, grow, and have support through scaffolding.

For more details on how learning stages in math should progress, check out my post on Geometry learning with Van Hiele levels.  This shows specific examples of how students progress through each scaffolded level as math learners.  Here is an additional post on theVan Hiele Levels as well for Geometry teachers.

We can teach toward a deeper understanding of math concepts if we keep these facts in mind.  The student brain is an amazing thing!  As we know more and more about how we process new learning, we can teach more strategically!
 
Boaler recommends some specific techniques to help build these basic skills. These include a teaching strategy called number talks, addition fact activities, multiplication fact activities, and math cards.   All of these activities help students learn math facts, while they do something they enjoy, not fear!
 
Did any of these insights surprise you? How is your teaching aligning with strategies specifically for math?  Let us know in the comments below!

​Chances are rigor sparks a feeling for you, maybe good or maybe bad. There seems to be a positive definition of "rigor" out there, but also a negative one. 
 
Merriam-Webster Dictionary defines rigor as:
 
1a (1) : harsh inflexibility in opinion, temper, or judgment : severity (2) : the quality of being unyielding or inflexible : strictness (3) : severity of life : austerity
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Harsh inflexibility seems incredibly negative to me, and is definitely not something I would ever want to encourage in a classroom.

According to Edutopia, however, we need a new definition of rigor.  “Rigor is the result of work that challenges students' thinking in new and interesting ways. It occurs when they are encouraged toward a sophisticated understanding of fundamental ideas and are driven by curiosity to discover what they don't know.”  

Healthy Rigor
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Since there are negative definitions of rigor, it’s important that we differentiate and continue implementing the positive attributes of rigor.  As a result of providing positive rigorous instruction, our students are challenged to think critically about the topic, and develop a more in-depth understanding. 

Positive rigor also encourages confidence in the classroom.  Confidence leads to creativity.  Once students are more confident in a topic, they will naturally gravitate towards thinking outside the box on the given topic.  
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Rigor in learning is, simply put, powerful.

Can they handle it?

Listen, kids may whine at first when you have higher standards and require them to push through more challenging coursework.  But they truly can do it!  It’s hard to not feel guilty for leveling up your game.  The complaining has led me to question so many times whether I was pushing too hard or expecting too much.  But if you just stick with it, it turns out they will accept that you are a tough teacher and that you believe they can do it!

Their coaches push them to run and require a lot of them, and they are not allowed to complain!  They can do the same in school.  Don’t be afraid to keep your expectations high.  Of course, you will need to differentiate and reach every student.  So I am not saying to make your demands on the kids unreasonable.  You’ll know what a student can truly do, and be sure that you are aware of their differences.  But keeping the level of healthy rigor high benefits everyone.

Remember that a whiny attitude at first is just a way of testing.  Are you going to cave and say “oh you’re right, that is too hard for you” or will you stick to your guns and have them give it a try?
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The reaction of kids to “test” the expectations reminds me of a video I saw a couple of years ago about parenting teens.  It compared teenagers to riders on a roller coaster.  When the ride crew comes around and pushes the bar down tight on your lap, what do you do?  Of course you push back up to test it.  But deep down, you are hoping it will hold steady.  You know you need that clear expectation, that you don’t want too much freedom.  You are hoping someone will be steady, clear, and not budge when you need that.  I think about that video often and I feel that it relates to so many aspects of dealing with teenagers and kids.

How to Blend Inquiry, Creativity, and RIGOR
 
NCTM shares the key to moving towards rigorous instruction as a big picture.  “Professional development experiences that model rigor through the use of rich tasks, rich discourse, and good questions allow teachers to experience rigorous instruction.”

Let's break that down!  Here are specific ways to incorporate healthy rigor:

RICH TASKS:

• Have students explore and discover properties for themselves.  For example, have them explore how they can arrange the desks in the room into a right triangle with a hypotenuse length of 7.  Let them explore, fail, and discover that only certain Pythagorean Triples exist!

 

• Ask your class to display the information from the lesson in a graphic note.  They’ll have to develop a layout to represent the big ideas and sketch visual memory triggers for the concepts.  You can offer them printed templates for additional guidance as needed.  (Because remember, we must differentiate to avoid the “harsh inflexibility” definition of rigor!)

 

RICH DISCOURSE:

• Encourage solid partner talk.  Let students chat through question prompts such as these critical thinking challenge questions.  They’ll have to clearly explain their reasoning, which strengthens understanding.  You’ll see the power of rigor in action!

 

• Require writing in math.  This is one of those ones that will induce whining, but it’s worth it.  Push through / ignore the complaining stage, then show them explicitly how to do it!  This Writing in Math Pack helps teach students how to navigate this challenge.

​GOOD QUESTIONS:

• Use strategic questioning.  This applies during lecture, during practice time, and on assessments.  Avoid multiple choice!  Try having students explain in words.  Prompt them to keep working when they are stuck, and phrase your hints as questions.  This takes practice!

 

• Try “always, sometimes, never” questioning to encourage all of these aspects of rigor to work together!  This type of questioning offers a rich task and also requires rich discourse.  Be sure to pair students up so they have to work together to determine whether each statement is “always true,” “sometimes true,” or “never true.”

​I just love finding new, brilliant ideas for organizing.  Some people have such creative ideas! And what better time to discover new ideas than right now when you may be thinking of getting organized for a fresh start for the upcoming school year?
 
I took some time to round up a few of my favorite ways to maintain organization throughout the school year and some new ideas that you might be interested in.  Hopefully they inspire you to stay organized

Class Periods

​Rainbow Colors and Class Periods
 
If you teach older students, it’s so easy to get your different class periods confused!  Brittany, from The Colorado Classroom, shares how she used RAINBOW colors to organize everything in her middle school classroom.  Not only does she color code everything, she uses colors in RAINBOW order, so it’s easy to follow and remember! 
 
By color-coding everything from their reward jars to homework graphs, Brittany is able to easily and quickly discern one period from another!  She shares, “...it eased my own levels of chaos and anxiety by creating a system of organization and structure that I could easily manage, and that my brain instantly enjoyed.  I happen to function well and enjoy seeing things in color; maybe you will too.”  Just think of what you can do with all that free mental space and time if you give this a try!

Grading

If you teach multiple classes and are still searching for an efficient way to grade and keep track of papers, then this idea is for you!
 
**  Sarah, from Tales of a High School Math Teacher, has tried numerous ways to organize grading papers, and shares her favorite one.  She uses a Fold-N-File from Thirty-One Bags.  In each section, she has a folder for each class, and then within each folder she has an “In” folder and an “Out” folder.  With this system, she can keep track of what needs to be graded and what’s ready to pass back for each class. 
 
**  Another awesome grading tip is to use color to “Grade at a Glance.”  Read how Leah hacks her google classroom assignments so that she does not even have to open each student’s file and wait for it to load.
 
**  If you want to try grading notebooks, my biggest tip is to walk around to grade them during a test.  It saves so much time, plus saves your back from having to cart crates of notebooks home!  More about that here: Grading Notebooks

Teacher Planner

If you don’t have a go-to teacher binder with everything you need, you are missing out!  If your teacher binder isn’t neatly organized, personalized, or aesthetically pleasing, then you are seriously missing out!!
 
Kristin, from One Stop Teacher Shop,  shares how she puts together the PERFECT teacher binder.   She includes wonderful ideas of tabs and individual pages you might want to include, depending on your needs, such as weekly lesson plans, small group lesson plans, class lists, and even charts to keep track of grading.

Classroom Jobs

​Classroom jobs are the ultimate way to give you a little boost in staying neat and organized! Brynn Allison, from Literary Maven, shares her brilliant ideas for classroom jobs in the secondary classroom.  Here are just a few of my favorites that will give you a leg up on organization:
 

• Filing clerk - If you keep student work or writing portfolios or have some kind of mailbox system for returning student work, have a student file these papers.
• Homework checker - If you assign nightly homework, have a student collect it. If you collect homework at the end of the week, but check to see if it is done daily, have a student stamp the assignments for completion or check off names on a check list.
• Supplies - Instead of students asking you for a pencil, a piece of paper, or a tissue, have one student in charge of these materials. If all of these things are already out in your classroom and accessible to all students, have a students restock when supplies are low and alert you when more supplies need to be purchased.

Using Your Door Area

**  Noelle, from Maneuvering the Middle, shares a bunch of awesome tips for Middle School Organization.  An ingenious and simple trick she shares is attaching a metal file folder on the door.  Place handouts they may need in the folder.  It’s easy to grab their warm-ups, doodle notes, or worksheets on the way in!
 
**  Another great door tip is to stick a “supplies needed” list in the window by the classroom door.  This helps kids see at a glance what they should grab from their lockers to bring to each class period today!

File Cabinet

I love Kate’s way of reorganizing her file cabinet!  It looks AMAZING and is such a needed investment of time.  This would save hours spent hunting for the sheets of paper that got thrown here and stuffed there during the chaos of the previous year!

Transitions

​Andrea’s tips for managing transitions are amazing.  Having smooth transitions can be a real game changer.  My favorite one is to have a “code word” of the day!  These creative solutions are worth a read!

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