Math Instruction and PWCS

Thank you all for the warm welcome I was given and I’m honored to be able to share comments on educational issues that are of importance to our community and across the nation.  Whenever I examine an educational issue I strive to find as much research as possible to inform my opinions and decisions.  I believe in the power and usefulness of good research as a tool to make the best decisions for my own children, and to help me, as an educator, to empower other parents to make strong decisions as well.  Notice I said PARENTS.  That’s right, I see the relationship between schools and parents as an interdependent cyclic flow of support and information, where parents have the ultimate say.  I hope you will find this to be a refreshing, back to basics approach for reforming public schools, especially from an educator, and I look forward to interacting with you.  So let’s get to it!

I was asked recently to comment on math instruction, particularly on the inability of students to understand how to perform basic mathematical functions.  The perception of this particular inquirer, and of many others who ask this question, is that the public schools are not teaching the basic concepts that the rest of us grew up learning.  It just so happens that Prince William County, the county in which I reside, is struggling to address (or avoid addressing) this very issue.  Last night, at the invitation of School Board Chairman Milton Johns, parents had the opportunity to address the school board about their concerns and about an option to opt-out of Math Investigations, the conceptual curriculum currently being used in the schools.  I had the pleasure of communicating with Mr. Johns on another issue several weeks ago and he vowed then to continue his efforts to improve the standing of parents in the eyes of the district.  This invitation is a commendable step in the right direction.  Back to math…

The debate comes down to a difference in opinion concerning the most effective way to teach math; by focusing on procedural knowledge (traditional/computational math) or conceptual knowledge (new/fuzzy/Chicago, Math Investigations/Everyday Math, etc).  Hiebert and Lefevre (1986) defined conceptual knowledge as steeped in understanding of how numbers relate and why, while traditional math teaches memorization of otherwise meaningless facts.  Star (2007) argued this definition to be insufficient and that the assumption that “procedures learned without connections to concepts are necessarily and by definition rote” to be a fallacy. 

The reality is that not all students were learning, understanding and maintaining an interest in mathematics using traditional methods.  Some students master concepts differently than others, and for students who struggle with traditional math methods, conceptual approaches are beneficial.  This is not breaking news and is not unique to the math world or to basic concepts of instructional style variation such as class seating, size, or teaching method.  The obvious reaction to raising student achievement after realizing that some kids aren’t getting it is to differentiate instruction.  Herein lies the problem.  Instead of differentiating, or successfully differentiating, there has simply been a flop to a new approach.  The new approach, like the old, works for some but not all. 

The research on math instruction is inconclusive.  Sadly, that’s often the situation due to weak methods, questionable origin of studies (funding motivation) and an inability to replicate research findings in alternative settings.  The most compelling evidence at this time suggests that a mixed method approach to instruction, or differentiated instructional style is best.  The National Research Council (NRC) in 2001 suggested that certain concepts or “strands of mathematical proficiency” should be taught using traditional methods in order to ensure “traditional fluency” while reinforcing the use of the skill in a conceptual way. 

Some parents in PWCS feel that their children are not benefiting from the use of conceptual math and they want their children using only traditional methods.  In the School Board’s good intentioned push to raise achievement among a subset of students, the students who were already doing well were forgotten, or assumed to be able to achieve using any method of instruction.  This isn’t true, and parents of higher level achievers are not happy.  Parents support an opt-out option that would allow them the choice to place their children in the traditional math program.  Teachers, administrators and board members say that traditional math is still taught along side the conceptual curriculum, yet parents say when they show their children the “right” way to do math at home, the children act as though they’ve never seen it. 

A true blended approach that uses traditional methods supplemented with conceptual instruction to further engage children and to reach those children who don’t catch on using the traditional approach should serve the needs of all, but clearly from the statements given by teachers last night, the blended approach is not being implemented in all or even most classrooms.  Regardless, it is ultimately a parent’s right and decision to decide the best way in which their children will learn.

This is the place where a strong, functioning partnership built out of mutual respect and trust could really flourish between parents and teachers.  Teachers, working in service to and in consideration of the needs and desires of the students and parents in regard to educational decisions and outcomes,  could align with parents, working in support of the needs of the teacher in service to their children.  This is exactly the kind of parent partnership I want to assist in building.  Alas, it isn’t happening now, at least not in Prince William County. 

Teachers and administrators are lining up on the battle lines to oppose the wishes of parents who want their students to be taught using traditional math methods.  This dangerous and counterproductive pitting of teachers against parents undermines the mission of the schools, regardless of the subject area or method of instruction and is reflective of the larger problem in Prince William County;  parents are seen as a nuisance by teachers and administrators who perceive themselves more adept, more qualified and ultimately more in control of what decisions are made for children.  Certainly that is not the view of all teachers and administrators, but of many, and is reflective of the entire beaurocracy that is PWCS. 

Below are some of the concerns raised by teachers and administrators at last night’s meeting.

 

“Having an opt out option doesn’t do students justice.”

“Higher level math ability requires understanding.”

“Parents should let the teachers and administrators decide what is best for students because they have the training, professional development and expertise to make the decision.”

‘Parents are spectators and should behave accordingly.’

‘The School Board shouldn’t waste time addressing the demands of a handful of parents.’

 

In defense of these teachers, I will just repeat that the organization reflects the sentiments of the administration and at least a few school board members (Which is a few too many, wake up elected officials!  You answer to parents, and to voters, and I for one am tired of having career politicians use the school board as a stepping stone to other, unrelated political positions without regard for the importance or seriousness of the job.)  In response to those same teachers and administrators, I would assert that years of schooling and professional development training (of which I have a substantial amount myself) do not qualify you to make decisions for or trump decisions of parents.  Professional credentials prepare one to advise and serve as a resource to parents as the PARENTS make the appropriate decisions for their children.  One of the teachers commented that parents would not presume to make decisions for their children’s doctors.  Not true.  Doctors, like teachers and others, serve to advise parents and encourage them in the way they think is right, but again, the ultimate decision making power belongs to the parents.  Even the medical community gets this.  Educators seem to be wrapped up in a self-prescribed dominance that isn’t allowed to exist in this country;  a fact of which they are unaware.  Perhaps some of the passionate energy that was spent insulting the rights and ability of parents to make adequate and appropriate decisions for their children could have been more effectively used in lobbying the parents through sincere concern and appreciation for their desire for what meets the individual needs of their children.  If parents actually saw a demonstration of sincere concern in pursuit of mutually agreeable compromises, I’m sure many would find themselves much more trusting of the teachers and administrators. 

I don’t disagree with the teachers that some of those parents could have children who could do well in a truly blended or even a pure conceptual program, but the definition of “well” varies in the minds of parents and teachers, and ultimately it is the parent, not the school/teacher/administrator or school board that has autonomy over the child.  That is aside from what educators, myself included, recommend as the “best”. 

Having an opt out option doesn’t do justice?  Certain parents have identified their students as not performing to their ability under conceptual math instruction.  That is no different than certain parents identifying their students as not performing to their ability under traditional instructional methods.  PWCS administration embraces the latter and rejects the former, while defending this position with statements such as “higher level math ability requires understanding.”  I think that’s a DUH.  For parents who are asking for a traditional math option for their students, that is exactly what they are supporting and upholding. 

If parents were asking that the conceptual program be completely abandoned then I would have concern for those students who are performing better on the “new” math program.  That’s not what they are asking.  They are asking for an option so that the students who do well under conceptual math can enjoy those benefits while their children receive the math instruction that they, as parents, feel is best for their children.  Win/Win. 

The truth is, parents who are asking to opt out of conceptual math will produce children who are high functioning math students for reasons outside of this discussion; ability to reinforce traditional methods at home, overall commitment to and monitoring of their children’s academic success, and because they are children of high functioning, successful adults.  The misplaced concern on the part of teachers and administrators over the damage that will be caused to these children at the hand of their “spectator” parents is a waste of time and energy. 

As for the concern that several teachers expressed over having to plan multiple lessons and use multiple materials, I can only say that special education teachers have been doing this for years.  If any teachers have concerns over how that process works, I’m sure their dedicated colleagues would be happy to assist, or perhaps the county will add this valuable professional development training to their list of credentials.  Differentiated instruction, when provided correctly, works and it works to address the needs of all kids. 

Parents deserve and expect choice.  Not every desire of every individual parent can be met at all times, but I can assure you that every effort should be made to find away to do just that, EVERY TIME.  The dissatisfaction of a  parent should be a most regrettable condition that the public schools should face and should only have to exist after all avenues of compromise have been explored.  Educators and school board members are accountable to parents.  Parents trust their board members and administrators to make decisions for their children, but that decision making power is not absolute, and it is on loan from the parents to the school.  At the point when a parent has a concern and thinks that his/her child is not being served in the best way, then that parent’s concern should be seriously and immediately addressed.  PERIOD. 

I would suggest that PWCS conduct a needs assessment in order to get an idea of how many parents would consider exercising the opt-out option for Math Investigations conceptual math curriculum.  Once the district has a better understanding of just how many parents want their children taught using only traditional methods, then a decision can be made on how to proceed.  If the numbers are small, differentiated instruction within the classroom could be sufficient to satisfy the needs of both groups within the same class.  If the numbers are substantial, perhaps some teachers would be assigned traditional methods classes while others teach conceptual classes.  Students would register for one or the other just like any other registration choice.  What an opportunity this would present for PWCS to come to some clear conclusion on the true merit of Math Investigations; three research groups, students in traditional and conceptual curricula and a third group using the mixed method approach that many administrators and teachers purport to use already.  Control for parental motivation and a few other potential intervening variables and THAT would be some good light reading.