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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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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?


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Tangible Parting Gifts

I can’t believe the year has gone by so quickly!  It’s already the end of May and there’s only one week left for final exams.  While my time at Salesianum School was short, it will be remembered.  I have memories that will last me a lifetime.

My memories are those that made me laugh, yell, admire, love, and befriend!  Any high school math teacher can relate to the mixed emotions that are experienced in (and out) of the classroom!  It’s not new.  Maybe some day I will share some specifics about those emotions and experiences.

Today, I want to share two tangible gifts I received this year.

1. A t-shirt with my name on the back.  The significance of the t-shirt is that the students labeled me as a teacher who “Keeps it real.”  I gave it to my students straight, no chaser, and they appreciated that.  If they asked questions, I did not sugar coat the answers (whether the questions were about math, friendship, dating, or life).  One of the parents purchased the t-shirts for the entire class (Thank you Mrs. R.).

T-shirt designed by 414-2.

Keepin’ it Real T-shirt designed by 414-2

2. A”K” shaped crepe.  One of my students hosted a French exchange student this year.  Toward the end of the 4th quarter my student earned a 92.2.  He needed a 92.5 to get an “A.”  The exchange student asked me to boost the student’s grade.  I told him I would if he would make me some food using an authentic french recipe.  So they made crepes (the french exchange student used his mother’s recipe – or so he said he did).  It was delicious, so I will deliver on my word.  He was a good student so I would have bumped him .3 points anyway (especially since he missed a few days of school while he was away at France as an American exchange student).

K-shaped crepe made by French Exchange student and his host

K-shaped crepe made by French Exchange student and his host

These are two of the tangible gifts I received this year.  The intangible gifts are too many to name here.  But to name a few I gained friendships, respect, knowledge, love, life-lessons, memories, and so much more.  I will miss my students, but they will always be close in my memories.


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Seven Secrets of How to Study Math and Science | Citywide Math and Science Institute

Seven Secrets of How to Study

Seven Secrets of How to Study Dr. Stephen Jones

 

As the school year comes to a close, remember to review your study strategies, skills, and habits in preparation of your final exams.  Read this blog about studying for math and science subjects and learn new ways to improve your grades.

Seven Secrets of How to Study Math and Science | Citywide Math and Science Institute.


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Bridging the Gap Between Arithmetic and Algebra

Copied from DragoArt.com

Copied from DragoArt.com

I have been teaching college level precalculus for several years.  A running theme of concern has been the lack of preparedness of my students for the course.  The struggling students somehow place into the course, but clearly are not prepared.  My assessment is that the students’ basic algebra skills are weak.  But what happens when a student takes algebra for the first time, but are not prepared?  Why are some students ready for algebra and some students struggle with the basic algebraic concepts covered in Pre-algebra or Algebra 1 courses?  What do you do as a teacher when you are faced with the challenge of bridging the gap between arithmetic and algebra?  How do you incorporate these concepts into your lessons without losing algebra “teaching time?”

This is an issue many Algebra 1 teachers face.  The common concern is that students taking Algebra 1 lack basic arithmetic skills.  But these skills are necessary for success in Algebra 1.  For example, many students struggle with adding fractions.  What happens when those same students have to solve equations with rational expressions?  If they have not mastered adding fractions, they will not be able to solve equations with rational expressions or they will experience difficulty when faced with these problems.

To me the answer is clear… Teach students so that they master basic arithmetic skills before they enter Algebra 1.  This charge is for elementary school teachers.  Here is the reality…  This is not always accomplished.  Elementary school teachers probably have their reasons for why this is not happening, across the board.  In the meantime, students are required to take Algebra 1 with whatever skills they have acquired.  This presents a problem to secondary teachers who have students entering Algebra 1 lacking the basic skills needed to learn and master basic algebra concepts.

How do you bridge that gap as an Algebra 1 teacher?  What does that bridge look like?  How do you help these students without hindering the advancement of the students who were fortunate to have mastered these skills?

These are very valid questions with many valid answers.  What are your thoughts?  What have you done in this situation?