Tag Archives: Mathematics

How Does Math Make You Feel?

Session 1 - Concept Map

Well, I hope math doesn’t make you feel like the Stanford University freshmen (see the concept map, above) who were interviewed for the OpenEdX course entitled How to Learn Math.  You might think anyone who was accepted into Stanford would be good at math (and feel good about their abilities), but not so.  In fact, the professor (Jo Boaler) includes in the first class session an interview with a scientist from the UK who, when awarded a medal by the Queen, still harbored feelings of math inadequacy.

Many thanks to Karl Fisch, for his blog post that pointed me in the direction of this class.  One minute I was reading about Karl’s introductory assignment for his students and parents, and the next thing I knew I was signing up for the class.  This is just up my alley and I am really enjoying it.  (Oh, and did I mention, the class is free!)

The concept map is one of my first assignments.  After listening to the students talk about their school math experiences,  I created the concept map to capture the essence of their responses.  I think it came out pretty well.  I’m interested to see what some of the other 20,000 (!) students came up with and if anyone had a different take.  Back to class!

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Kindergarten Assessments

K_Verbal_Assessment  K_Written_Assessment

Above are the two Kindergarten assessments I created.  Although my initial purpose for the assessments is to use them with older students, I attempted to make them appropriate for Kindergartners.  Full disclosure: I am a secondary math teacher, not an elementary teacher.  However, I have read Knowing and Teaching Elementary Mathematics by Liping Ma (fantastic book, I highly recommend it – thanks Jean M.!)   I have also been researching elementary math tasks so I can better help a 6th grade student with whom I am  working.  I’m sure I will learn more as I use the assessments.

Why two assessments?  Well, some standards need to be assessed verbally (e.g., counting to 100 or counting out loud).  Furthermore, I may want to see and hear the student’s performance.  Specifically:  How fluently is he adding or subtracting?  Where is he hesitating?  Even the written assessments are not intended to be completed in isolation; I plan to watch the student as he completes the problems.  Again, I will see where he is fluent and where he hesitates or skips a problem.  I will gain insight into any misconceptions as well as skills he may be lacking, which will help me decide the concepts I will need to  reteach.

Although the assessments may appear to be cast in stone, my intent is to use them more flexibly.  So, (and I’m thinking out loud here) after the student demonstrates she can count by 1 to 20 or 30, I would stop and ask her to count by 1 from some higher number to 100 (which actually incorporates the second Kindergarten standard, K.CC.A.2).  Ideally, I would then follow up with a question to see if she could explain the counting pattern.

Also, if a student is really struggling with a problem, I would intervene.  First I would start by asking some guiding questions to see if he could then figure it out.  I might change the problem to be simpler or let him skip it all together.  After all, these are not tests; I just want to know where the holes are.  It is paramount that I keep it positive, that I keep the student talking to me.  Teaching is as much art as it is science.  I need to know when to push and when to back off.  I need to know my students.

Still, there may be better ways to assess students on these standards.  If you have suggestions for how to improve the assessments, I hope you will leave a comment!  (I have already seen some assessments that elegantly group multiple standards in a single task, which are intriguing.  Although, as my purpose is to determine which concepts students have yet to master, it might be easier to assess each standard individually.  I’m still thinking about this.)

Finally, I consider these assessments to be “first drafts” and plan to modify or change them after I use them and see how they work.  What do you think?  Am I on the right track?

Start at the beginning.

Mathematics.  That word … it makes so many people cringe.  Not me.  I’m someone who always loved math, even though advanced math didn’t necessarily come easily.  So, it was natural that I looked to mathematics when my career seemed isolating and empty and I decided I needed a change.  But not just any change; I wanted to do something I was passionate about, something worthwhile.  I had been volunteering in middle school math classrooms and saw a need for helping students understand math.  Fast-forward a few years, and I have a master’s degree and a secondary math teaching credential.  I can’t decide – do I teach middle school or high school?  Or, do I go back to school so I can be a math specialist in elementary schools because that’s where the trains leave the tracks, if you know what I mean; that’s where kids decide “I can’t do math.”

Then, I’m sent in a new direction by a chance encounter and a phrase that resonated: teach students math all over again, starting with Kindergarten.  This seemed to encompass both my desire to help students comprehend math AND my personal need to know the entire curriculum – from Kindergarten through Calculus.  A broad mathematical understanding is necessary for helping students regardless of grade level, and I knew it would allow me to ascertain what skills and concepts students were lacking as well as how best to position them for the mathematics that lay ahead.

This blog is the account of my journey to understand (and understand how to teach) the entire K-12 math curriculum using the Common Core State Standards (CCSS) as both a framework and a jumping off point.  To begin with, I plan to create a series of CCSS-based assessments that, when given to students who need help, will illuminate missing foundation concepts (beginning  with Kindergarten) and provide a starting point for targeted assistance.  In the end, I hope to have a complete and useful set of assessments, plenty of online references, and a collection of tasks and lessons full of authentic and challenging problems.  Oh, and by-the-way, I’ll also have an intuitive and connected understanding of the whole K-12 mathematics arc.  This should be fun.  All I need now is someone to collaborate with.  Are you with me?  We start at the beginning.  We begin with Kindergarten…