A May 1982 EdWeek article, entitled Research and Reports, featured a study conducted at the University of Missouri-Columbia on the teaching of 4th grade math.
The researchers, Thomas Good and Douglas Grouws, examined the effects of an experimental mathematics program, which they developed from their previous research findings on effective teachers. Using more than 1,000 4th-grade students and 40 teachers from 27 schools, the researchers divided the schools into “treatment” and “control” groups.
They found the students whose teachers used the experimental program improved more than the students whose teachers continued to teach in their usual manner. They found that those following the new program spent more time explaining the meaning of the material and engaged their students in less seatwork than the control group. They also found that the teachers who used the program reviewed 92% of the material, contrasted by 62% of the teachers in the control group. They also required 63% more mental computation than the control teachers.
Why Haven’t We Found The Best Route?
Since this was the case then, it remains a mystery as to why we haven’t settled on the best route to teach mathematics and move ahead by now. But we haven’t. Hence, the arrival of the Common Core Standards. The question of dividing fractions emerges as one of the many sticking points. Usually taught as “invert and multiply”, the skill is learned. Ask most folks why that is so, and they return a blank stare. From BrainPOP.com:
When you divide fractions, you actually do the same thing as you would when multiplying fractions, but you flip one of the fractions upside down.
For example, if you are multiplying 3/7 x 2/5, you would multiply the numerators and the denominators, to get (3 x 2) / (7 x 5), or, 6/35. If you were dividing 3/7 by 2/3, you would flip one of the fractions upside down:
3/7 ÷ 2/3 = 3/7 x 3/2 = 9/14
Flip one of the fractions upside down? Is it important to know why we are allowed to do so? So it was with interest we read the August 12th , 2014 Curriculum Matters post entitled, With Fractions, Common-Core Training Goes Beyond ‘Invert and Multiply’. Author Liana Heitin considered the methods used in the Common Core for the teaching of mathematics. In her article a question was raised by a professor emerita of mathematics from the University of California at Berkeley who claimed it was artificially intricate and complex. The Common Core “goes beyond ‘invert and multiply.’”
Local Control: Opportunity for an Essential Conversation
The questions about the methods required for dividing fractions is as good place as any to make the space for an essential conversation.
- Why should we be teaching mathematical processes? In what grades?
- How does what we believe mesh with the expectations of the standards we are presently expected to meet? What steps do we need to take to narrow the gap between them?
- How will we manage to teach these mathematical processes in the similar ways in every classroom?
- Have our secondary math teachers noted any new and different methods that could be used in the earlier years that could contribute to secondary math success?
- Are the processes “artificially intricate and complex” if they are taught at the correct developmental levels?
- And, in this specific case, is it important to know why a process is done, or is it satisfactory to remember the rule?
Stark differences exist between the conversations that take place in a district with a high poverty rate and a low graduation rate and a district with a low poverty rate and a high graduation rate. Stark differences also exist between the conversations that take place where math coordinators or department chairs exist and where there are none. And stark differences exist between the conversations in districts with changing leadership and those with steady leadership. Context matters.
Local Conversation is Paramount
No matter the feelings that exist around the Common Core Standards, until and unless things change, we are implementing them. Students and teachers are evaluated by the assessments that accompany them. This is the juncture where local control and student achievement meet. No matter the standards and their assessment, the local conversation is paramount. There have been studies, programs, and methods that have provided the routes to student success in all areas. In the study mentioned above, note that two of the Common Core mathematical practices, understanding the meaning and being able to do mental math, are included. These ideas are not new ones. But with established national standards, in a country where local differences are so profound, ongoing local explanatory and exploratory conversations are required.
Meeting the needs of the students in wealthy districts like Darien, Connecticut or Scarsdale New York is a very different task from meeting the needs of the students in low wealth North and West Bolivar School Districts in Mississippi. The political belief is that setting a national standards’ bar is the answer to improving education for all students. Some say it is a daunting charge, and some say it is an unattainable one. What remains true is local implementation requires consideration of what we know, what we don’t know, how we will implement necessary changes, and how we will measure them while moving toward the new expected standard.
The Call To Lead
This #tbt points to a larger issue than math instruction. Once again it is a call for leadership. Curricular leaders in every district must guide the process. What is taught and how it is taught crosses all disciplines present the choice for leaders: feeling directed and powerless or required to be bold and creative. Teachers will be impacted by the choice we make....so, too, will students.
Conversations naturally unearth all the reasons for resistance. Bringing them out of the dark presents the opportunity for conversations to become safe examinations of the issues. John P. Kotter and Dan S. Cohen, in their book The Heart of Change, write:
The emotions that undermine change include anger, false pride, pessimism, arrogance, cynicism, panic, exhaustion, insecurity, and anxiety. The facilitating emotions include faith, trust, optimism, urgency, reality-based pride, passion, excitement, hope, and enthusiasm (p. 180).
Creating the space for safe and honest conversations to take place is the role of leaders. Knowing when and how to move beyond those emotionally charged conversations into responsive and responsible action is the delicate dance of leadership. The questioning will continue but it cannot become a delaying or deterring mechanism. Hearing the needs of the faculty and finding doors that can be opened to offer them the support they need is key. The attitude with which any change is met can be influenced by the manner in which the leader takes the “tiger by the tail.” We may not be in control of what presents itself, but we do control the manner in which we deal with it.
Kotter, John P., Cohen, Dan S. (2002) The Heart of Change: Real-Life Stories of How People Change Their Organizations. Boston: Harvard Business School Press
The opinions expressed in Leadership 360 are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.