Tag Archives: Classroom

6. Attend to Precision; Precision

Gottlieb Wilhelm von Liebnitz

6. Attend to Precision.

The mathematically proficient student will need the ability to communicate precisely.  This is true for both verbal and written communication.  The core standards for mathematics requires students to do much more writing about problem solving than has been necessary in the past.

While this concept confuses many parents, politicians and even teachers, it is a helpful tool for sorting through problems and remembering the steps taken to solve them.  Most classroom subjects require note-taking.  The notes can be useful for review and test preparation, but their greatest benefit may be in the memory enhancement provided simply by the act of writing as well as hearing a lesson.  Good note-taking requires listening or reading closely, and then separating the truly important information from the rest. The good note taker, along with the proficient mathematician, will then be able to take those nuggets of information and communicate them in complete sentences; a requirement of proficiency standard 6.

Understanding which information is truly “the most important,” and being able to communicate it requires the ability to use clear and accurate definitions.  Students cannot clearly communicate multiplication if they do not understand the meaning of the words multiplier, multiplicand and product.  They cannot describe measurements without being able to clearly define the difference between area and volume.  True proficiency requires the ability to define concepts and processes. Additionally, students must recognize and be able to define or describe the meaning of mathematical symbols. Math is a language filled with symbols. The inability to understand mathematical symbols makes problem solving impossible; just as the inability to understand letters and punctuation makes reading impossible.

Labels are another key to mathematical precision.  Maps, coordinate planes, measurements and graphs are all incomprehensible without labels.  The labels must be precise, and they must be used in a manner that makes it clear what item is being labeled. Students who fail to use labels appropriately will find it impossible to communicate their work.

Finally, the mathematically proficient student will need to synthesize all of these abilities, along with the ability to calculate accurately and efficiently. Once their problem is solved they will need to be able to communicate their process and answer via carefully formulated explanations. This action alone may point to flaws in their logic, causing a review and reworking of the problem at hand.  This is accomplished through the careful examination of solutions through the magnifying lens of the definitions and constraints inherent in the problem itself.  When looked at in this light it becomes apparent precise communication is key to not only the fulfulling of an important standard, but to the basics of problem solving using the language of math.

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Filed under Education, Homeschoolers, National Common Core Standards, Primary Education, Proficiency Standards

A True Challenge

jim

Reflection on the challenge posed by implementation of the National Common Core Standards seems an appropriate first entry.  It WILL be a challange.

Nationwide, textbooks based on the common core will be missing from most classrooms. This issue could go on for years in some districts.  Teachers and homeschoolers will need to read and comprehend the unpacked standards.  This will give them an opportunity to develop concrete objectives.

“Multiple resources” will be required.  Students need access to accurate background information, meaningful practice and objective driven assessments. Teachers need the progress measurement data provided by objective based assessments.  Additionally, logs of lesson plans, materials used, classroom activities, practice opportunities and assessments will be important for communication with students, parents and administrators; in an era of student performance based evaluation.

Books geared toward “teaching the test” will be thrown together quickly.  The publishers may find it difficult to actually teach critical thinking; a vital component of the common core.

I am part of a website team at commoncoremath.net.  The site is committed to providing teachers a laddered approach to teaching the common core math standards.  At commoncoremath.net standards have already been unpacked and objectives developed.  Critical thinking and writing skills are woven throughout the curricula.  Classroom differentiation is facilitated by the availability of all materials, across all grade levels for all members, (membership is only $20.95 per year.)

commoncoremath.net provides thousands of pages of lessons, practice materials, assessments, tracking forms and other resources for print, computer or smartboard use.  It is the ultimate “teacher’s helper” for these changing times.

Good luck from a sixth grade teacher!

James Wheeler – commoncoremath.net

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Filed under Education, Homeschoolers, National Common Core Standards, Primary Education