With a Mathematics Perspective:


Karen J. Bennett

CTER Program at University of Illinois


Tom Anderson, Instructor


Innovations in scheduling seem to be a popular reform for schools across the country.  It is estimated that the number of schools that have implemented some version of block scheduling ranges from 10 to 25 percent, while many more districts are considering the concept. (The Center for Education Reform : "Scheduling: On the Block" Nov. 1996)  But my research has shown block scheduling to be very controversial.  There are strong opinions on both sides of this issue.  It's creators are touring the country, proclaiming it's virtues, and  some schools are "models" for its success.   Yet many websites have sprung up, in strong opposition to it, denouncing the claims made and campaigning to prevent its implementation in their local schools!  Both sides are passionate in their viewpoint. 

My school district is researching block scheduling and considering its implementation.  How does the evidence stack up?  Does one side prevail?   As a Mathematics teacher, I wondered what such a plan would mean for me and my students should my district decide to implement block scheduling.


What is block scheduling?

Block scheduling is typically a restructuring of the daily schedule to create longer units of time for each class.  Traditionally, six to eight classes meet for 45 - 55 minutes each day.  Block scheduling creates fewer classes each day, meeting for longer periods of time.  There are almost as many variations as there are schools implementing the block!! 

One of the most common versions, the 4X4 Plan (promoted by David Hottenstein and Robert Lynn Canady) makes the standard year long courses into half year long courses of 90 minutes in length.  Students take two classes in the morning and two in the afternoon with a new schedule for all teachers and students midyear.   In a variation , the 4X4 A/B Plan is similar to the above except that classes meet every-other-day all year long.  Teachers meet with half of their students each day.

Some plans do not have the same schedule daily -- some courses meet Mondays, Wednesdays, and Fridays for 90 minutes and then on Tuesdays and Thursdays for 180 minutes.  Some districts have periods in which certain classes meet daily for a short time, then the longer courses on the block begin.  I encountered a wide variety of plans in my research.  Examples included: the San Francisco Urban Plan, the Kentucky Plan, a 5X5 plan, the George School Plan, and a 9-13 plan.

Dr. Joseph Carroll's "Copernican Plan" is an extremely different schedule.  It has students attending only two classes per day.  Each class is 180 minutes long.  Then the course is completed in only 30 school days. 

The variations seem endless.  Schools can design their own plans.

What, specifically, are the concerns of teachers and students of mathematics?

The National Council of Teachers of Mathematics Instructional Issues Advisory Committee discussed Block scheduling.  The Committee defined issues on a web page without drawing conclusions since research is sparse and there is such a wide variety of schedules that can be employed. 

The mathematics-related issues posed by NCTM's Committee are:

  1. How is the amount of instructional time impacted by block scheduling?
  2. What is the impact of block scheduling on Advanced Placement Classes and Advanced Placement Exams?
  3. Since students could conceivably take four mathematics courses by the end of their sophomore year in the semesterized block, what is the impact of block scheduling on the NCTM's recommendation that students take mathematics each year in grades 9 - 12? 
  4. What is the impact of block scheduling on college entrance examinations and other standardized test scores?
  5. What is the impact of extended breaks between sequential courses, such as Algebra I and II or between any two mathematics courses?  Do extended breaks in time between mathematics courses impact on student performance?  On the semesterized block schedule, should students be allowed to take one mathematics course in the fall and then no mathematics until three semesters later? [NCTM 1997]

While researching these and other questions, I discovered that there are definitely two distinct viewpoints to the Block Scheduling DEBATE.


Why change from the traditional six- or seven-period day?  

Block scheduling advocates cite the grueling pace of a typical school day - An average student is in eight different locations pursuing eight different activities during the six and a half hour school day.  Teachers are also taxed with multiple preparations for five classes, dealing with 125 -180 students each term.   Dr. Joseph Carroll claims that this "hectic, impersonal, inefficient instructional environment" provides inadequate time to deeply explore issues and discourages variety in learning activities.  Carroll and other advocates of Block Scheduling, claim that teachers are often unable to develop relationships with their students in the traditional system.  Scheduling on the block system allows longer, more concentrated classes.  Longer class periods mean more flexibility.  The old lecture style can be supplemented (or replaced with) cooperative learning, team teaching, multidisciplinary classes, projects, labs, or field work.  The environment allows more opportunities for variety in teaching techniques, as well as more time for interaction -- both between students and student-to-teacher.

Proponents claim that Block Scheduling will create a "less pressured, more intimate atmosphere in the school, creating a place where children are excited to learn and teachers are inspired to teach." (CER Scheduling on the Block")  Better attendance, higher grades and lower dropout rates are some of the benefits Block Scheduling fosters, according to believers.

Advocates claim that less time between classes means more time IN class.  Since discipline problems seem to occur between classes, discipline referrals should decrease.   Less time would be wasted on start of class procedures.

According to Canady and Rettig, writers of "The Power of Innovative Scheduling", alternative scheduling allows students to enroll in a greater number and variety of elective courses.  Under the Block, students who fail a course can retake it earlier.  Block scheduling makes it possible for students to accelerate through a program and even earn a "free year of college", according to Clarence Edwards.   Edwards writes that being able to take more courses during their HS career could equate to less courses in college.  Consider, for example, that students have 8 periods each day, seven classes and lunch.   Under the block schedule, students can take 8 classes and lunch.  The block provides them with an "extra class".


What are the results of implementing the block?  What does research/experience show?

Advocates claim that the benefits of this system include:

Many schools report positive changes after implementing some version of block scheduling.  Some examples:

Asheboro High School in Asheboro, NC has become a leading advocate of the block schedule movement.  Over a four year period, 6000 visitors observed their block schedule and two summer workshops with over 600 participants each were held at the school.  According to principal, Mike Warren, students have benefited from the change with more choices and more course work over the four years.  Teachers and students like the lower number of classes and student-teacher ratio.  While there has been, "no dramatic changes in test scores", more students are taking "harder" course work and there has been increased enrollment in AP courses.  The results of a 1997 Survey of 25 North Carolina High Schools on a 4 X 4 block schedule find that "students and teachers find the block schedule to be as good as or better than the traditional schedule among and for all types of students".

Angola High School in Angola, Indiana also claims Block Scheduling a success.  At the Annual Meeting of the Midwestern Educational Research Association, Angola High School Science teacher, Dave Snyder presented a summary of data analysis done after two years on the block.  The successes included highly significant improvement in grade point averages, improvement in semester exams and increases in the number of students on the honor roll.  ACT scores improved, SAT remained the same, and AP scores dropped slightly.  Snyder's report boasts high satisfaction among students, faculty and parents.  

In New Jersey, Jackson Memorial High School's On-Line website for Block Scheduling cites the highlights of a survey of schools using the block.  On their web page announcing the decision of the district to change to a block schedule, advantages expected include: a significant decrease in the number of failures, an increase in overall grade point averages, a decrease in disciplinary referrals, and declining dropout rates.  According to JMHS's web page, a survey of schools on the block report that retention of knowledge is "not a problem" for schools using this schedule "over a number of years".  Morale is improved in both staff and students.  Attendance by both teachers and students improved.  (Students like having less classes at one time.   Teachers enjoy the greater amount of preparation time and lower student-to-teacher ratio under the block.  Many feel they can be more creative and more effective in the greater blocks of time.)  [JMHS online Nov.1999]

Positive attitudes toward Block Scheduling abound on the web.   In a Professional Development Discussion of the Teacher Education Center Archive on Block Scheduling, teachers heralded the system as "refreshing" and "not a fad that will ever leave our building".  Many caution about the need for staff retraining in the use of the extended time.  Some recommended training videos and workshops by name.  Tere Burton submitted a report to the AFT Online Conference on Block Scheduling on April 11, 1995.  In it she describes the largely positive attitudes of students and teachers toward the block in her school.  She also insists that teachers should be allowed input into the scheduling decisions and training time to visit schools or consult with practicing block users. 

But the web is not the only source for positive feedback about Block Scheduling.  I consulted colleagues for their personal opinions and experiences.   Megan Forness, a graduate student in U of I's CTER program who is currently employed by the Illinois State Board of Education, taught mathematics in an 8 block system at Rochester High School during school year 1998-1999.  Under this system, classes alternated days.  Megan enjoyed the opportunity to incorporate at least 4 or 5 different activities into each period, but found that it took a lot of planning.  The 8 block schedule made it possible for her to add variety to her lessons.  With the increased time, she was able to insert video and internet applications into her lessons.  She reports that the 8-block worked well for group activities and cooperative learning. 

Another CTER student, Jolynn Plato, a middle school teacher in the Springfield Public Schools, used block scheduling for three years at her former job in a parochial school.  She loved planning for the 90 minute periods, since there were less preps per week.  She also reported that teachers enjoyed the extra time for class reinforcement.

In summary, block scheduling has received a lot of positive reports.  

Block Scheduling sounds fantastic!  How could anyone be against it? 


The OTHER SIDE OF THE STORY...            

What do Block Scheduling opponents say?

For every fan of Block Scheduling, a detractor can be found.  Many websites exist to educate (and persuade) parents, teachers and concerned citizens about the issue.  These sites certainly have an agenda, acting as propaganda against the movement.  For each positive aspect listed by proponents, the opposition has a counterpoint.  It is a testament to their passionate concern and involvement that many of these individuals maintain elaborate websites to further their cause.

In Viera, Florida, a group of block scheduling opponents, led by Jon Brooker, publish a website concerning Block Scheduling.  The Block Scheduling Sources and Connections site encourages concerned parents and citizens to do their own research into the matter and to be actively involved in the decision-making.  To encourage serious analysis and not "thoughtless cheerleading", Brooker's site includes hyperlinks to sites across the U.S. which "range from rabid pro or con ranting to the sweet voice of moderation and reason".  He claims that the "con" viewpoint is seldom offered at schools where the block is being considered.  Brooker encourages attendance at school board meetings to question the wisdom of a decision made to change to the block.

Another fierce opponent of Block Scheduling, Michael Sabia, a mathematics teacher at the Wissahickon School District in suburban Philadelphia, Pennsylvania, fights against block scheduling.  Sabia masters a website called Block Scheduling's House of Problems. He is also the contact person for a group called Parents for Academic Excellence.  His site reiterates the points made by fellow challengers.  Sabia also discourages usage of the Block Scheduling plan. 

Block scheduling opponents maintain that there is very little "hard" data behind the glowing reports put forth by its Advocates.  Jeff Lindsay, a concerned parent, engineer and former educator, is the webmaster of a well-known website against block scheduling ("The Case Against Block Scheduling" ) Lindsay questions the validity of research that uses small subject samples or short periods of time. Concerning Dr. Carroll's report on his Copernican Plan, Lindsay writes,

"I have not seen Dr. Carroll publish standardized test data for any of these schools - just the results of internal tests and grades.  I am also not aware of any peer-reviewed publication by Dr. Carroll on his work, though it has received much attention in education magazines." 

On his webpage, Lindsay questions the acceptance of results that have not been scientifically demonstrated in larger, more thorough studies, and questions the methodology of Carroll's work.  Brooker echoes Lindsay's concerns about the lack of "hard" evidence supporting block scheduling.  Speaking to the Brevard County school board in Viera, Florida, Brooker asked,

"... why can't (we find) even one well-designed, peer-reviewed, longitudinal study showing that in the long run Block Scheduling actually helps academic performance?" 

**Interestingly, the only scientific analysis of data that I could find for Block scheduling was the Angola, IN study.  After my research, I became more critical in my own review of information and noticed that this study was for a brief two year period of time.  Two years is barely enough time to negate the Hawthorne Effect (the burst of enthusiasm in response to the "newness" of a project that often leads to temporary improvements).

Opponents challenge the "advantages" that Block Scheduling proponents claim.  In Brevard County's web article, "The Mythology of the 90-Minute Classroom" these advantages called "The Myths" are answered with "The Reality" ... Summarizing some examples:

The same arguments in response to the supposed advantages are made on most opponents websites.  In different format, the site makes many of the same points and concurs with the others.

Block Scheduling's detractors have an additional "list".  They are concerned that these problems are not addressed by proponents:


Donald Lofland, a physicist and educator, wrote   "PowerLearning:  Memory and Learning Techniques for Personal Power".   His Memory theory is explained in a link from Michael Sabia's Block Scheduling House of Problems website.   Some components of his theory follow: 

People tend to remember more from the beginning of an event. (e.g. the first part of a class, or first people we are introduced to, first students we taught )  This is called the primacy effect. We also tend to remember better what happens at the end.  This is called the recency effect.  The idea that you will be more able to recall that which is strange, unusual, humorous or out-of-context more easily is another factor in memory recall known as the "Von Restorff effect."  Psychologist and educator, Tony Buzan, in "Making the Most of Your Mind" lists five main factors which assist memory recall.  Primacy, Recency, and Outstandingness (Lofland's Von Restorff effect) are the first three on the list.  Buzan adds Linking, a concept that maintains recollection of something is easier when it is connected to previous knowledge.  And, Buzan's fifth factor is Review.   According to Buzan, this means that anything which is reviewed will tend to be more firmly lodged in the brain. 

If these factors affect learning, then it is helpful to organize time in the best way to increase retention of information.  Classes that are shorter and more often may give students more opportunity to increase memory.  There are more starts (and ends) on a traditional schedule with more frequent classes running year long.  Block scheduling would provide less primacy and recency events.   This may have a detrimental effect on student recall. 

Frank N. Dempster writes of a learning phenomenon he calls, "the Spacing Effect" in an article which appeared in American Psychologist in 1988.  Dempster found that

"With total study time equated, two or more opportunities to study the same material are much more effective than a single opportunity." 

"To summarize, more frequent use of properly spaced reviews and tests in the classroom can dramatically improve classroom learning and retention.  In addition, research suggests that spaced repetitions can foster time-on-task and help students develop and sustain positive attitudes toward school and learning."  [Dempster 1988]

Likewise, H.J. Walberg concurs with Dempster's findings.   Two spaced presentations are about twice as effective as two massed presentations (concentrated, possibly in one session).  The difference between them increasing as the frequency of the repetition increases.  Dempster claims this effect does not apply only to rote learning and memorization, but that "memory is of central importance to any complex intellectual activity" and as such, the spacing effect may aid students in integrating knowledge and in constructing abstract paradigms.  

Applying this phenomenon to block scheduling, the traditional schedule would allow spaced reviews over a period of days, rather than in a single 90 minute period of time.  If spacing increases recall, the block schedule may not be as effective as the traditional schedule. 

Dr. Frank Y. H. Wang agrees.  Wang , President of Saxon Publishers, which publishes the Saxon Math series, expressed concern for the effectiveness of teaching mathematics under the block.  He issued a statement about block scheduling and retention.   Jeff Lindsay quotes Dr. Wang's 1996 letter on his webpage:

"Saxon publishers does not advocate the use of block scheduling.  If you are considering whether to implement block scheduling, we suggest you do not.  We believe that children learn most effectively when they are exposed to concepts in small, easily understandable pieces called increments and when new concepts and skills are reviewed continuously."

"the frequency of students' exposure to the subject matter is much diminished from a traditional system where students meet every day." [Wang 1996]


Part of the problem with teaching math in extended periods of time, experts believe, is the decreased amount of homework.  In an extended class period, at least a portion of what would have been homework is done during class.  While this may be a benefit in the eyes of some students and parents, mathematics educators express concern.  Homework is a vital component in students' success.  Students must practice their skills.  Recent research backs this up.   In a study of homework and student achievement, psychologists obtained data sets from over 700 "triads", which they define to be a teacher, at least one student, and one parent of that student.  Homework behavior and attitudes were analyzed for grades 2 through 12.  Findings revealed, not surprisingly, that the more homework students complete, particularly between grades six and twelve, the better they perform in school.    [Cooper, March 1999]

Homework is a "necessary evil" whose benefits are derived when the work is done at home, according to Parenting Magazine's Adair Lara.  Quoting Maurice Elias, a clinical and school psychologist at Rutgers University, Lara writes "Homework teaches children how to work independently.   They're learning actively, not passively, which they just can't do in group instruction."  James R. Nuttall, Ph.D., a developmental psychologist advises parental involvement and encouragement in an article for Effective Parenting's webpage called "The Homework Battle".   Nuttal begins with "a simple truth about education here in the United States or anywhere else in the industrialized world.  Doing homework well is the key to succeeding in school."


Is there any scientific block schedule research concerning mathematics  specifically?

The largest scientific study comparing objective student performance of students on the block schedule with students in the traditional, full-year classes was done in Canada.  The Raphael study of Math was printed in the Canadian Journal of Education in 1986 in an article titled, "Debunking the semestering myth".   Students were tested on several different mathematical areas: number systems, algebra computation and skills, equations and inequalities, analytical geometry, trigonometry, function, probability and statistics.  In every area, the year long class average scores are higher than the semester-long class average scores, whether math is their area of specialization or not. 

Abstract: "Advantages claimed for semester organization of secondary shcools were examined using data from a probability sample of 250 mathematics classrooms in 80 Ontario schools.   Achievement and attitude data were collected from 5280 students in the course of the Second International Mathematics Study, and it was determined that 94 of the classes were taught in half the school year, ie. by semesters.  Teachers in semester schools were likely to report use of a greater variety of instructional materials.   Suggestions reported in the literature of better student attitudes and achievement were not supported, and performance of Grade 12 and 13 students in semestered classes was significantly lower than those in year-long classes. Teachers in semester schools reported comparable coverage of mathematics content, but fewer hours of instruction in their courses.  Number of years of teaching experience was not correlated with student achievement in semester schools, but a positive correlation was observed in year-long classes.  Lower achievement in semester mathematics classes was observed with no advantage in student attitudes."   [Canadian Journal of Education  1986]

Gordon Gore also studied the extensive data from British Columbia.  One of his reports reviews twelfth grade Provincial exam results in 1996.  Specifically, mathematics mean scores of full-year students were 69.41% compared to 64.63%  for semester students and 62.85% for quarter students.  Looking at grades given on the math exam, 24% of full-year students received A's, 14% of semester students did so, and only 11% of quarter students.  While performance for quarter students dropped, this was not necessarily reflected in the marks they received in the courses!  

Some advocates of block scheduling, dismiss the Canadian studies as "not applicable".  An American study (with a much smaller sample of students) finds similar results concerning the effects of the block schedule on the learning of mathematics.

Dr. Mike Wronkovich, of the Coventry School District in Ohio performed a year long study on the effects of block scheduling in the area of mathematics.  His results, which appeared in the December 1997 issue of the NASSP Bulletin showed findings similar to those of the Canadian studies.  

students who studied Algebra 1, Geometry and Algebra 2 under block scheduling performed significantly below those studying the same subjects under traditional scheduling on a early college math achievement test.

But, unlike the Canadian results, Wronkovich found that students enjoyed math more in the block!

Finally, for those students actively involved in block classes, they expressed over and over in the comments a greater enjoyment of class time.  The qualitative impression is that students who choose the block schedule for math find the lessons are presented in a more palatable manner.  The data, however, suggest that they may not be learning as much or have the material as well mastered. [ Wronkovich 1999, quoted by Lindsay, March 2000]



While there may be many reasons for a school to adopt block scheduling, educational advantage in the area of mathematics does not appear to be one of them.

More often than not, instructional time is not increased.  Two fifty minute class periods are replaced with one 90 minute block of time.  The longer time does not seem to be beneficial in practice, even when teachers are well-trained to vary their methods of instruction.  Some schools have had to add an Algebra III course to their curriculum in order to cover the concepts that were "cut" from the curriculum in order to fit into the block schedule.  This is sure to produce confusion when viewing transcripts!

Many schools operating under the block schedule have to schedule "review" classes in May before the AP exams.  Some vary their schedule to make the class end nearer the time for the exam.  Many districts have appealed to the College Board (AP Board) asking for a January exam.  AP has denied this request, thus far, because of the relatively few students that are affected by this schedule.  But I wondered as I read this, if this doesn't prove that students working on the block schedule ARE struggling with retaining the information - contrary to what proponents claim.

The NCTM recommendation that students take math all four years of high school is challenging under the block system.  It is conceivable that a student could finish the entire curriculum in two years!  A two year "lay off" from mathematics study of any kind would not be helpful to students wishing to continue their education, particularly in the sciences.  NCTM's recommendation was designed to help students keep their skills honed.  Even if they successfully complete the sequence of courses, the gaps of time between them will be detrimental.

There is not a lot of scientific data regarding college entrance exams and standardized test scores.  The jury is still out.  But if the Canadian studies' results continue to hold true, it does not look good for mathematics achievement under the block schedule.

My Much Considered, Personal Perspective:

While the advantages of Block Scheduling (less preps, less students, more planning time each day) sound good, I am not willing to take the risks that I believe block scheduling offers.  The negatives that I have discovered through my research would not allow me to support the change in good conscience.  It would not be fair to my students.

The benefits in terms of fewer discipline problems, improved GPAs?, increasing numbers on the honor roll, and increased number of courses that can be taken are all lovely.  But none of these alter the disturbing fact that, according to the best scientific research currently available, kids do not seem to learn math as well under this system!!

As teachers are being held more and more accountable for the performance of their students, I am adamant that we should not create a situation that seems harmful to our students.  There are enough difficult factors in education today.

If the district does decide to go to Block Scheduling, I would use my research and whatever influence I could muster, to push for a modified block that allows math classes to continue to meet daily for 40 - 50 minutes as they have traditionally done.


A List of Resources Used: