NCTM Process Standards: Has the Focus Changed?

Today, mathematics teacher are encouraged to employ NCTM Process Standards in their lessons.  Though they are not standards to be taught by themselves, the Process Standards are meant to guide lesson planning and implementation so that students develop these important process skills.  The NCTM recognizes these skills are vital for students to succeed throughout school and later in life.  However, I do not feel this was always the case.

When I was in grade school, I only remember a focus on two of these process standards: problem solving and reasoning and proof.  In fact, the primary focus was on problem solving.  The only time I faced reasoning and proof was in geometry when we focused on proofs of theories.  Though I still managed to develop many of these process skills on my own, I am pleased to see they are actively being incorporated into every day lessons now. 

NCTM Process Standards: Why Are They Important?

Just as NCTM Content Standards outline material and topics that students should be able to solve as they move through school, NCTM Process Standards outlines skills that students should be able to use as they work through the Content Standards.  If you are not familiar with the Process Standards, here is a brief description as outlined in the Intervention in School and Clinic journal:

1)       Problem solving – solving problems individually or in groups, reading vocabulary words in the problems, “discussing and presenting solutions”, and “coming up with the whole-group problem solution” (Lee and Herner-Patnode, 2007, p.123).

2)      Reasoning – Linguistic approaches, playing games using flash cards, creating dictionaries, and keeping notebooks (Lee and Herner-Patnode, 2007, p.123).

3)      Communication – “Small-group and whole-class discussions,” “individual journal writing,” and notebooks (Lee and Herner-Patnode, 2007, p.123).

4)      Connection – “Providing everyday life contexts,” “using every day materials,” and “using familiar everyday words to help describe, but not in place of, vocabulary” (Lee and Herner-Patnode, 2007, p.123)

5)      Representation – “Using picture dictionaries,” “making and keeping vocabulary cards,” “displaying words on tag boards of different colors,” acting out vocabulary words,” and creating cartoons (Lee and Herner-Patnode, 2007, p.123).

Though these process standards come from the National Council of Teachers of Mathematics, the skills they encourage are valuable in all subjects and eventually in adult life.

Reference:

Lee, H., & Herner-Patnode, L. (2007). Teaching mathematics vocabulary to diverse learners. Intervention in School and Clinic, 43(2), 121-126.

Assessment Experiences

Recently I was asked what type of assessment I encountered most often while I was taught mathematics throughout my school years.  Before I began taking classes toward my teaching degree and credentials, this question would have been easy to answer.  The only types of assessment I experienced was written tests, written homework, and working problems on the board. 

Now I find this question incredibly difficult to answer because I am aware of all the different types of informal assessment that I never would have noticed as a child.  It is very possible that my teachers carried out many types of informal assessment just by observing me as I work and listening to my answers in class.  In fact, I am positive they did exactly that.  However, I don’t know that it was to the extent that informal assessment is carried out today.  Frequently it was the answer that mattered, not the process.  Today, I find much more emphasis on performance assessment of various types and the student must explain the why and how, not just provide the answer.  Honestly, I think this is one of the most important changes that could occur in mathematics instruction because being able to clearly explain your reasoning is a skill that can lead to a lifetime of success. 

The Joy of Geometry

Last time I wrote, I praised the skill and teaching ability of my algebra teacher from high school.  He was a great man and taught me many things.  There is a great distinction I need to make though.  Just because my algebra teacher was my favorite math teacher does not mean that algebra was my favorite math standard!  No.  My favorite standard was geometry. 

See, I am a visual person.  I like pictures, colors, and patterns.  Geometry presented me with all that and more.  Even more, how all the angles and lines related to each other fascinated me.  I loved how knowing one or two measurements allowed me to find everything else.  That doesn’t mean that geometry came easy for me, because it certainly didn’t, but I still loved it. 

Is there a topic that you loved even though it wasn’t easy?

Teaching Mathematics: Then and Now

In my journey to become a teacher, I am fascinated with how much teaching has changed since I was in elementary school.  Perhaps the largest changes I have noticed involve language arts and mathematics.  Since mathematics was always a strong skill of mine, I find the changes to this subject the most interesting!  Can you remember how you were taught mathematics in school?

Most of my memories of learning mathematics take place in third and fourth grade and high school.  In third and fourth grade, I remember focusing on multiplication and long division.  I remember a brief explanation regarding repeated addition and repeated subtraction, but then we focused on memorization.  We had what felt like tons of worksheets, timed tests, drills, and assignments.  In high school, I remember having the best algebra teacher in the world.  He used visual aids and thoroughly explained the reasoning behind everything and why it worked. Though we had to memorize formulas, we knew why the formulas worked. 

Looking at mathematics instruction now, teachers focus more on reasoning, problem solving, and why something works rather than memorization and drills. This is more beneficial for students because they can apply these skills to other subjects and real life events.  I feel that my algebra instructor was a forward thinking teacher and part of the transition between the era of rote memorization and today’s critical thinking and problem solving and I thank goodness I was his student.  After all, it is my algebra teacher that made me want to be a middle school math teacher in the first place!