Math Education Concepts

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Quick and Dirty Guide to CCSS Math

Written For Tutors

In all my years of tutoring (20+) I have yet to go through one full year without a major issue arising, in mathematics education, that tutors have to face.  This year (and over the past few years) that issue has been Common Core State Standards (CCSS).  Many tutors want to know how to help their students when standards have changed, or become more uniform across states.  These changes have resulted in the development of mathematics curriculum and use of new texts in many school districts.  However, although many states have adopted the CCSS, the standards do not require a specific curriculum or text.  (This leaves the door wide open for companies to sell their products claiming to be aligned with the standards.)  To make matters more confusing, many districts can make their own decisions about what materials to use to teach their students.  This creates a struggle for many tutors: the materials changed suddenly, the expectations are higher for students, and parents can’t begin to explain why their child struggles with the content.

In light of this, I have good news… for tutors!  The standards are for teachers to worry about; your concern is helping your students learn the material being taught.  Below I listed a few tips/strategies for helping your students during the CCSS era.  Many of the tips here are not original or new, but may be more relevant to the expectations placed upon students as a result of the CCSS.  So, let’s get going…

Please feel free to add to these or modify them to accommodate your students’ needs.  I hope this is helpful and will alleviate some stress!

  • Help students think critically and analytically – higher order thinking is an expectation
  • The standards are for teachers to use during instruction – no need to feel compelled to include them in your instruction
  • Know and understand the standards so you can help your students – know what your students are expected to do and understand
  • Tutor with the same confidence you had before CCSS adoptions – students will trust you more if they feel you are confident
  • Get your students accustomed to justifying their answers – if your students can justify their answers, then, most likely, they understand the concept taught
  • Change the format of the problems so you can check for understanding – students should understand the concept behind the problem rather than just the procedure for solving it
  • Know the language used in the standards – encourage your students to use and know it as well
  • Speak positively instead of negatively about the standards – if you resist the change, so will your students, but they will hurt in the end
  • Don’t panic – or your students will panic as well
  • Relax – so your students can relax and learn

Resources:

  1. Common Core State Standards
  2. Common Core Math Standards
  3. National Council of Teachers of Mathematics (NCTM)
  4. National Research Council’s “Adding it Up”
  5. EdReports.org
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Own Your Education

When I woke up this morning the last memory I had was of a dream that occurred only minutes, maybe seconds earlier.  I was standing in an elevator in a school district administration building.  The elevator was crowded and to my left stood a mother and her teenage (or pre-teen) daughter.  They were having a conversation and quite naturally, I was listening.  The conversation had something to do with the girl selecting a high school for the coming year.  She didn’t want to participate fully in the selection process.  Like so many young people today, she wanted her mother to make the decision for her.  Well that conversation got my blood boiling, but in a good way… I think.  This is what happened next (I’m paraphrasing, but you’ll get the point)…

I turned to the young lady and told her that she should go and get involved in the selection process.  I told her to go to the schools, tour the classrooms, and get a feel for the environment.  I reminded her that she should select the place that would feel conducive to learning for her!  Finally, I said “you will be here for eight hours each day, not your mother, you will have to sit in these classes all day, not your mother, and you will have to eat the food, not your mother!  Own your education!”  By that, I meant that she should take control of her education by making those important decisions that would impact her education journey.

Then I woke up.  It was one of those dreams that felt real, like I was on that elevator and speaking with that family.  The truth is that is exactly what I would tell young people today, “own your education.”  This is the one thing we have some control over, the one decision many parents allow children to weigh in on.  The one decision that could determine their future career, lifestyle, path!  Granted, young people do need some guidance and direction, but should have some autonomy when it comes to deciding where they will attend high school.


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My Summers, Lately

I had the best summer at camp last year and I’m looking forward to camp this year.  Yes, I was at camp last year, Math Corps Philly Summer Camp, with beautiful people having fun and calling it “work.”  I was the Program Coordinator/Dean of Students for a camp of about 20 middle school students, 10 high school students, and 3 college students.  I primarily took care of paper work and making sure the students ate well and were taken care of (that’s really everyone’s job).

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The highlight of every day was watching the students have fun, bond, learn, and grow by the end of camp.  You would have to be there to fully understand the magnitude of love that was shared throughout the camp.  By the end of camp there were hugs, tears, pictures, tears, and more hugs.  Everyone would be missed until next time.

So now it’s January and I am recruiting students for camp again.  No, this isn’t my pitch for camp recruitment.  I’m just sharing the continued joys I’m looking forward to this year and the years that follow.  But, in case you are interested, feel free to check out our website for pictures, videos and more information about how I spend my summers.


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Thinking Mathematically

When you are passionate about something, you tend to relate almost everything else to that “thing.”  For me, that “thing” is math.  I relate almost everything in my life to math.  Whether it’s my hair (curl pattern, texture, etc.), my dishes (the way they are stacked in my cabinets), the highway (the number of car spaces between my car and the car in front of me), or even the shadow on my dining room wall (it’s a reflection of my light fixture and it’s shaped like a sine curve reflected across the x-axis).

I think mathematically… I count the number of steps it takes to get to the bottom of the stairs, I count the number of tile squares it takes to create the pattern on my bathroom floor, I count the nails in the walls, and I count the number of holes there are in the design of my laundry basket.

So, do I think mathematically because I happen to enjoy math or do I enjoy math because I think mathematically?  Either way, I am passionate about mathematics and mathematical concepts and ideas.  And as much as I try to hide behind my desk (and avoid teaching), I still get excited when having conversations about all things math!  Thanks for the brief conversation S. from NC!


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Concept-Based Learning and Math

Concept-based learning is not a new idea, but one that should get far more attention than what I’ve seen.  I recently found the following definition on “What Is IB?”

“Concept based learning is about big transferable ideas that transcend time, place, situation. Content just focuses on facts while concept focuses on making sense of those facts and the world around us. Content based teaching may not get beyond information transmission/superficial learning. Concepts are a way to organize and make sense of learning.”

When thinking about teaching and learning mathematics, concept-based learning makes the most sense.  Why? Situations change, contexts change, numerical values change, students change, etc.  If a concept is taught and learned, then changing the context or situation will not affect how to apply a concept.

I recently helped a student prepare for the math section of the upcoming SAT.  One question in the practice book showed the graph of a line with no numbers.  The question asked the student to select the equation of the line.  If the student knew the concept of graphs of lines (slopes, y-intercepts, etc.) then they would have been able to solve the problem easily.  They could determine whether the slope was positive or negative and whether the y-intercept was positive or negative.  Without the understanding of these concepts, the student was not able to answer the question.  Once I explained the concepts and details, then the student understood.

Concept-based learning should be a central focus when teaching mathematics.  Otherwise, students will continue to stumble over content when situations and contexts change.

What are your thoughts on concept based learning?