Wednesday, September 26, 2012

Teach Math Well: Learning Update

I continue to find my Tuesday night math class to be both informative and inspiring.  The pace of the course is a perfect match for my busy school schedule, and the content continues to serve as both affirmation and challenge for my current teaching program.

After a thoughtful YouTube film related to the benefits and practice of formative assessment, our professor, Mary Corkery, presented highlights from a webinar that was presented by Dr. Paul Riccomini, President of The Division for Learning Disabilities (DLD), one of 17 special interest groups of the Council for Exceptional Children (CEC), the largest international professional organization dedicated to improving educational outcomes for individuals with exceptionalities, including both students with disabilities and the gifted.

The webinar discussion served to both affirm and challenge the math program I currently teach to my fourth grade students. As I expected, Riccomini emphasized the need for positive, math-friendly teaching environments where all professionals exhibit confidence, knowledge and positive language related to math teaching and students’ ability to learn. He supported the notion that more time should be spent on strengthening teachers’ understanding of math concepts and knowledge since many elementary school teachers lack a strong foundation in math.

As he listed the attributes of a successful math program, the one area he mentioned that I would like to increase is students’ time to think and talk aloud with regard to math problem solving.  Due to class sizes, students often don’t have time to talk out a problem or question aloud, especially students who may take more time to process or verbalize their thoughts. Since I have many volunteers, teaching assistants and specialist teachers working in my class, I hope to use our collective resources to give students more time, in small groups, to thoughtfully discuss and solve meaningful math problems related to the Massachusetts State Frameworks which include the Common Core Standards.

I was pleased that recent updates in our system-wide math program reflect the six pieces of a successful math system including the following:

  • A Strong Belief System.
  • Assessment and Data.
  • Instructional Support.
  • Refinement of Instructional Supports.
  • High Quality Professional Development.

Our system has created greater opportunity for teachers to attend worthy math courses and conferences to boost their professional repertoire in this regard. This movement towards greater differentiation with regard to professional development in math is serving to boost teachers’ knowledge and strength in that area.

Riccomini emphasized a tiered program with a strong emphasis on the core program which aligns well with our school system’s current movement towards increased RTI (response to intervention).  I was pleased and affirmed by his call for standards-based classrooms that actively engage in purposeful learning experiences that stimulate curiosity, enjoyment and deep understanding of the mathematical concepts. Too often, math activities are mundane, and I would like to move towards greater engagement and purpose in this regard.

He offered his ideal for the math lesson breakdown which included this list:
  • Fluency practice and homework review.
  • Standards focus.
  • Vocabulary (literacy is very important in mathematics).
  • Mini lesson-whole class instruction.
  • Work sessions - flexible grouping and small group intervention.
  • Closure and sharing.

The current program at my school includes the features above.  Fluency practice is often completed during transition times and morning work. Homework is often given via quick-feedback Internet sites such as
That Quiz, TutPup, SumDog or Xtra Math, all free, engaging math websites for young students. The standards are communicated via the classroom math website, social network and the unit/lesson introduction.  Vocabulary is practiced in a number of ways including the use of charts, crossword puzzles, the Frayer model and multimedia projects such as film.  I find that crossword puzzles elicit a lot of discussion when it comes to vocabulary thus enriching students use of mathematical language in a natural way.

The webinar supported my colleague Mike O’Connor’s notion that learning facts is “mental push-ups.”  He suggested that schools employ explicit, direct teaching to help all students attain fact mastery. Rather than “Mad Minutes,” he recommended that teachers carefully assess students' number sense and begin to build their fact fluency from early skills to later skills with targeted intervention. While listening to the webinar I created this assessment based on Riccomini’s research and other research I’ve done to begin a targeted program with my student who demonstrate little fact knowledge.  I’ll build a similar assessment and intervention for children who have mastered addition facts.

Not surprisingly, Ricomini relayed that fractions is the "biggest weakest area" in terms of math in the United States, and if students don't learn fractions well, they will have great difficulty grasping algebra. He stated that students don't realize that fractions are numbers, instead they think of a fraction as only "part of the whole." Rather than saying 1/3 is larger than 1/6, they should say that 1/3 is a greater amount of the whole than 1/6. He emphasized the use of a number line (with both negative and positive numbers) to build number sense in all areas including fractions because the number line explicitly shows quantities. He offered the article, "Developing Fractions Instruction for Kindergarten Through 8th Grade," as an excellent resource.  

Currently I am teaching measurement standards and the correct use of a ruler. I have noted to students that a ruler is a number line," but now, after the webinar, I'll explicitly use the ruler to guide students' efforts related to counting and marking specific fractions on the number line with this exercise. I also plan to take a recent measurement open response problem and revise it with a variety of rational numbers (not just integers) to give students the experience of using the ruler or number line to solve complex problems that involve fractions.

The Tuesday math class continues to invigorate my math instruction and knowledge, and I'll continue to share the highlights with those that read my blog. Please let me know if you have any links or thoughts related to the information above.