Why Singapore Math

In 1983, Singapore ranked 17/26 in TIMSS.  Singapore then adopted a new national curriculum for all schools.  In 1995, Singapore ranked 1/41.  Singapore has remained in the top 1 or 2 since.  Hong Kong SAR is the main challenger with Finland close.

Singapore has recently adopted a heavily revised curriculum that is more focused on problem-solving.  The impact of the revision, particularly on calculation/number sense, isn't clear at this time. "Singapore Math" refers to the 1994 revision, with modifications for California.

Singapore Math can be seen as having these distinguishing features:

  1.  Going in depth on a few topics for mastery learning
  2.  Extreme emphasis on building Number Sense
  3.  A coherent, longitudinal approach in the use of modeling to solve word problems

Instruction follows a basic sequence of Concrete - Pictorial - Abstract - Mental Math. One hour per day with little homework is employed.

Mental Math means that students learn to add, subtract, multiply, and divide internally.  Flash cards are barely known as existing!  Calculators are unnecessary.  For example, 15 is seen as 10+5, which means that students may determine internally that 9+6 = 9+(1+5) = (9+1)+5 = 10+5 = 15 or 28-13 = (28+2)-(13+2) = (20+10)-(10+5) = (20-10)+(10-5) = 15. One way isn't mandated, but students must explain their process.  In short, place value and the use of tens are paramount to an extent that is unknown in the United States.  Abstract algorithms such as multiply and carry or long division are delayed for as long as feasible.

Developing models, as precursor for algebra, follow an orderly progression, by doing 1-3 daily word problems.

     K-1 Manipulatives
        2 Base 10 blocks
     3-4 dots/disks
     5-6 Rectangles         

Each word problem is solved following the same form:  Model - Equation(s) - Sentence answer - (scratch area).  Neatness and completeness matter in this MES system.

One implication of Singapore Math is to ask parents not to help!  Americans teach the wrong methods too early.
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The above words are edited notes of a presentation by Corrine Khoo-Lieu (Palo Alto) of the Pi Project on March 28 in Los Angeles.  Extensive demonstrations of activities were performed.  One of several small training consultancies on Singapore Math.  Richard Bisk (Massachusetts) is another highly sought after consultant.
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The SmartMath software, written in Hong Kong, used in the CRO, mimics much of Singapore Math. If a district wanted to implement Singapore Math, a rollout works best, but K2 can be done easily at one time. 3-4-5 could follow year by year or one year after K2.

Alternative Attendance Measure in Instruction

Reducing cuts is important. However, contacting parents or student for excuses after a student's return makes less sense now than in the past.

Before a PLC (Professional Learning Community) emphasis, teachers would issue zeros for missing work if students cut. The reward for bad behavior was no work, followed by more poor behavior because students quickly realize that zero's force them to fail in a standard 0-100 point system, which creates more hassle and costs for the school system as a whole and dropouts. Now, students must complete their work: attendance is irrelevant for grading, but vital for learning. More subtlely, the joy of being sick goes away to the student. This approach has been used successfully in summer school for years: excuses are irrelevant. The metric that matters is attendance, not the reason. The three-days-to-change-a-cut rule remains somewhat useful for awards, but no reminders to students and parents to clear a cut need or should be made. Getting students to school is the issue, not asking them or parents for an excuse when they arrive or afterwards.

Furthermore, sadly, there is a correlation between poor attendance and disruptive behavior. Since students can be transferred at no, or little charge, to a County ACCESS High School after four full days of cuts, it actually behooves schools and the majority of students within them to have absences marked as cuts. It gives schools more flexibility in dealing with, frankly, dangerous students.  Reminding returned students or requiring excuses before students return to school is self-defeating and wasteful of everyone's time. It's merely going through the motions of improving attendance.

In short, attendance is the only issue. Excuses are irrelevant. Higher attendance does not result by administratively pressuring ourselves to reduce the number of marked cuts. The enemy to learning isn't cuts, but excused absences! Working this number down would have positive effects.

Possible Metric

a. ID the number of First Period Absences in last semester as a baseline.
b. ID the number of Full Day Absences in last semester as a baseline.
c. Record the number of First Period Absences and Full Day Absences this semester.
d. An increase in First Period, but a decrease in Full Day means a real system improvement has occurred.
e. Decrease/Increase in all absences is the obvious main statistic.
f. Trend the two numbers above and single period skips.

When Multiple Choice Becomes Continuous Assessment with Positive Reinforcement

Multiple-Choice, MC, assessments inhibit long term learning. As a rule, they may work for summative assessment, but not formative. Furthermore, in mathematics, since guessing can yield correct answers, false positives usually cloud software responses. As a result, more MC problems are needed for students to solve in online classes, which usually decelerates learning. One of the secrets of better adaptive math software, such as ALEKS and Carnegie Tutor, is that they employ only a few constructed response questions. They allow a student to show mastery faster than most multiple-choice programs which struggle to compensate for false positives; especially since quick guessing is a common strategy with low achieving students. MC programs generate unexpected student responses because they are too ready to help.  XLPrep and possibly Study Island, are examples of MC software that may frustrate student learning because their response to errors or successes don't demand that each student needs to want instruction at that moment and struggle through it! While at first counterintuitive, pretty instruction is merely a time-killer for many low-achieving students. ALEKS and SmartMath offer simple explanations only after a student, somewhat reluctantly, asks for it, knowing that he or she, will have to read to understand. This may also be a problem with the constructed-response software iPass. It's detailed instruction is beautiful, but students eyes wander during the videos, because they are forced to watched.

However, multiple-choice software doesn't have to suffer from the conventional maladies. In particular, SmartMath from Encyclopedia Brittanica (USA) and Planetii (Hong Kong) demands students answer 30 MC questions in a row without error! Random guessing is automatic test failure, not just a missed question. Students can earn stars, actually limited insurance, to save themselves from immediate failure by doing many problems correctly during earlier practice sessions. Adapting to a rapid train of MC questions seems to turn the problem of inhibited long term learning on its head. Instead of letting distractors interfere with their learning, students quickly seek them out to discard them in the search for a correct answer. Distractors seemingly concentrate thinking, not dissipate it. Finally, the active decision-making on choosing to earn zero to six stars, which allow 30 out of 30 to 30 out of 36 (a missed question generates an equally difficult question) involves the students responsibly in their own learning. They have to decide when to take the test because earning six stars takes a long time. This engagement and active self-assessment is the secret behind SmartMath, which allows issues with multiple-choice to evaporate.

After using many different brands of software in classrooms using during semester trials over the last four years, two programs have worked well together for full class coverage: SmartMath and ALEKS. The results of a quick assessment place students into SmartMath or ALEKS. While SmartMath has a rapid mastery option, students can take a Billy Madison approach: they try to spend only 1-2 weeks per level (six levels total) and start at Level One, which is a tough first grade! With cute, spinning avatars jumping for joy with correct answers, students march through the curriculum feeling their way through the inherent difficulties. As a subtle extra motivator, stressing that SmartMath was originally developed in Hong Kong also raises the importance of each individual's success. Students realize that they are being evaluated from an international perspective. Success matters more.

The Key Results of the NMAP Report.

The tables and what readers infer from them in the National Math Advisory Panel Report are what truly matters.

A streamlined curriculum means that mandated topics need not be 100% of a math course. This is the great unwritten benefit of the report. Without stating it, NMAP agrees with the Core Knowledge, CK, method of using a core curriculum: the core hovers around 50% of a course in a CK classroom. The actual percent of time spent on streamlined curriculum will depend on students and their groups, which is a difficult issue to address in print. This allows enrichment and remediation to occur in real-time, while staying on an acknowledged, understood national path.

The Benchmark Table is what regulates math instruction. The table implies that mastery learning be implemented within a streamlined curriculum and its assessment. It's about learning, not teaching!

The School Algebra Table, California Algebra 2 without conics, adjusts the pathways of the high school math curriculum, striking a balance between rigor and realism. Algebra 2 is absolutely necessary, but High School Geometry, isn't! Knowing how to determine the measures of inscribed angles isn't really vital. Yes, A1-G-A2 may be the standard and wonderful, but A1-A2 works.

All of the comments and responses on research methods, etc. are embarrassing. They really are beside the point. Words on research-based are merely buzz or rants of the chattering class, but a reasonable, streamlined curriculum that demands mastery learning - now that's something special. Are there any comments that the tables of the NMAP Report are unreasonable or a poor starting point? No. In short, opponents of the report, need to ask themselves: are we bricks in the wall? (with thanks to Pink Floyd)

Donation from Costa Mesa Community Foundation

Times are tough, but the people of the Costa Mesa Community Foundation believe in helping students stay in school by completing their math requirements - math failures equals dropouts.  Please thank them for helping sustain ALEKS use in Newport-Mesa. ALEKS is the fastest way to mastering math.

Embracing CHSPE Allows a Pathway to School Reform

The California High School Proficiency Exam, CHSPE, which is lawfully equivalent to a high school diploma for any purpose in California, serves as the linchpin for comprehensive, yet low-cost, school reform in California.  It accomplishes this through three critical benefits:

1. The CHSPE serves as graduation insurance for students as schools increase rigor.
   
2. The CHSPE helps implement an Early College, which improves college success.
   
3. The CHSPE allows students to take courses they want to take, which reduces dropouts.
   

Schools want to increase rigor. For example, Algebra 2 or three years of science could be graduation requirements. However, the very real risk of increasing dropouts makes this effort very risky. For a principal or superintendent to bet the future on the words of pundits or a few researchers claiming that more rigor also will magically reduce dropouts is foolhardy, but if a safety net presented itself that also enhances the transition of students to community colleges or vocations, then the vigorous deployment of not only rigorous courses, but also career-oriented courses with extra support for students starting community colleges could proceed reversibly. Reform need not mimic Cortez's burning of his ships. The California High School Proficiency Exam, CHSPE, offers each student graduation insurance, and therefore supplies an often ignored mechanism in gaining community support in reforming schools.

In brief, CHSPE-based reform helps solve the problems of many courses being too easy, students needing remedial courses in college, students not completing college, and high drop-out rates, with the possibility of improved API scores.

Increasing Rigor Flexibly

a. The high school must request a waiver from its district for added graduation requirements for incoming ninth graders.  For example, while different pathways to rigor exist, many graduation requirement sets would include either three years of both science and math or statements like Chemistry, Biology, Physics or Geometry, Algebra 2, Pre-Calculus or Algebra 1, Algebra 2, Statistics.  The requirement set could be modified each year, and hold for the entering class.

 

b. Similar to colleges stating graduation requirements for entering students, a high school would notify eighth graders that its requirements will be different than the standard in the district. Eighth graders would have the option of starting at another high school, if space is available. They also would be told that they could take the CHSPE in tenth grade and graduate early or stay in school with a special schedule, if they so chose after passing the CHSPE.

c. Graduation requirements could be modified for each entering class as feedback on student success and difficulties and results on increased rigor became available.  In particular, the choices that students make after taking the CHSPE and later, the actual results of those decisions would determine the effectiveness of this approach to high school reform.

CHSPE and Student Decision-Making

d.  Eight and ninth grade students would be informed that those who complete Algebra and two years of high school math strongly perform well on CHSPE and graduate early. Those who neglect studying flounder and struggle through four years of high school.

e. The CHSPE would voluntarily be taken in February and June during tenth grade. With a cost of nearly $100, students would be careful in taking it. There is no legal reason for a school to pay for the CHSPE. However, organizations such as a PTA could partially subsidize the fee.

f. Students who pass the CHSPE would enjoy these options:

• Simply stay in high school and graduate at the end of 12th grade.
• Graduate immediately with family permission.  This would allow a full community college course load with fees. However, student failure is likely. Early high school withdrawal could be effectively discouraged by the obvious benefits of the other choices. However, early withdrawal would serve students who want to start a non- or low-technical trade program or possibly those who seek a certificate program from a community college. 
  
• Complete, but do not file, school withdrawal papers.  Students would gain these benefits:

1. Able to take two community college classes without fees

2. Attend high school on a reduced schedule with study halls for college classes

3. Reduced schedule could include focused courses such as robotics or drama 

4. Reduced schedule could simply be independent study courses supporting college classes

5. Enjoy food and activities such as sports, which would be inappropriate for those NCAA-bound

• Students, who graduate early, would be welcome to reapply for admittance. There is no need to penalize students for making unfortunate choices that could be mitigated.
• Instruction in 11th and 12th grade would operate at higher levels than currently employed. Students who couldn't or wouldn't meet the standards could always opt-out by passing the CHSPE or transferring to another high school, if remediation proved ineffective.
• Students who cannot pass the CHSPE would be served as current students are. However, with, hopefully, fewer numbers they could be identified and focused on better than today.

The Opposite of Cynicism

In could be said that encouraging CHSPE is an improper way of increasing a school's graduation rate or decreasing it's dropout rate, but the opposite has been far worse for decades.  Although aware, very few California school officials tell parents and young adults of the CHSPE's availability because bodies are dollars in ADA districts.  Arguments against the CHSPE are self-serving, while arguments for the CHSPE are informational and grant options to students and parents.  It young adults another way, perhaps their only way, to succeed.  Explaining the benefits and disadvantages of the CHSPE is professional and proper.

In Basic Aid districts, not ADA districts, a student leaving school is close to revenue-neutral.

Note: CAHSEE vis a vis CHSPE

The CAHSEE is a necessary condition for awarding a high school diploma, as set by state law. The CHSPE is sufficient to be recognized as a diploma for ANY PURPOSE under state law.  The CAHSEE is easier than CHSPE because its tests lower level math standards.  In addition, the CHSPE includes an essay examination in its English componenent.

Let Successful CHSPE Students Walk in Graduation

Yes, the CHSPE is easier to earn than a district high school diploma, and from an initial, gut reaction, letting CHSPE students walk in graduation doesn't seem fair because they have accomplished less than most of the other students, but consider the advantages to all parties, and a 180 may be warranted!

Positive Reasons to Encourage Students to Walk

Don't let the best be the enemy of the better.  With 25% of students dropping out of school, it may be that most students taking and passing the CHSPE have a close to 50% chance of not graduating otherwise.  Walking through graduation may be their only motivation to even continue with their education. The CHSPE is an educational compromise. Passing it can be joyous; not a moment of regret. Save criticism for dropouts; especially since CHSPE students frequently plan to continue their studies at a community college. Students and their families should be legitimately proud of earning the CHSPE, and remember they are the foundation of education - they're called taxpayers and voters.

Early graduation is not rejection.  A school administration need not think that a student taking the CHSPE is rejecting them, the students are simply rejecting two more years of conventional school after completing eleven or twelve years.  In short, school leaders shouldn't take CHSPE results as reflecting poorly on them.  Passing CHSPE can be considered a vindication - students have succeeded early and are ready to move on; albeit not perfectly.  They shouldn't be punished for leaving the nest; nor should administers think they failed.

Motivate ninth and tenth graders.  The prospect of graduating school after 10th grade may help ninth and tenth graders try harder in math and language classes.  Seeing happy people move on in a graduation ceremony, not a second class disappearance, serves as a powerful image.  Hearing other students moan about not knowing enough math to pass the CHSPE will also have effects.  In Alt Ed, juniors perform better than sophomores because they see the end of school and the pleasures of walking in graduation.  The resulting success may even encourage them to stay!

Discourage pettiness.  Do many hard-working honor/AP students and their parents seriously claim that "the normal students" don't deserve to be in graduation?  Surely some do, but the complaints are ignored.  Similarly, would normal graduates strongly state that those CHSPE students have no right to walk in our procession?  It's absurd to believe they would.  Should administrators be petty for them?  Letting holders of CHSPE certificates walk brings joy with little cost to students who have been in the system for eleven years. In their mind, they have paid their dues to ed code. Advising that they stay in school is one thing.  Denying them a small benefit of completing state requirements truly seems inappropriate.

Acknowledge the academic truth.  How many at-risk graduates could pass the CHSPE anyway?  Many retake the CAHSEE several times and CHSPE is far more difficult.  Are conventional at-risk graduates actually more academically qualified?  Where's the evidence of this?  To err towards hurting people in this situation seems cruelly unwise.

Increase morale of instructors and staff.  Teaching young adults who don't want to be in school yields poor learning results.  Below Basic on CST's after a year of work is neither an honor for teachers nor students. Teachers may complain, but they also want to keep challenging students in Alt Ed. CHSPE students are in the highest quartile in Alt Ed. Yes, they should be encouraged to stay in school, but denied walking in graduation because they are more talented than other Alt Ed students?  Upon reflection, most teachers would praise walking and the benefits it indirectly grants to their classrooms.

Embrace the CHSPE.  There are many incredible and surprising advantages of students passing the CHSPE.  Setting the stage for increasing it's deployment is enhanced by letting students walk in graduation.

Legal Considerations to Let Students Walk



California law states that the CHSPE certificate is equivalent to a high school diploma FOR ANY PURPOSE to agencies operating under California law.  On the other hand, LEA's (e.g. school districts) have large sway in making policy under many precedents.  In short, parents could sue to allow their child to walk with reasonable grounds for success.  However, the proceedings will be messy and expensive and unproductive.  The issue really is just being able to walk in graduation.  It is simply too small an issue for an administration to fight considering the text of the state law.  Where is the compelling school need to circumvent state law?

To count requirements twice can be construed as an effort to violate state law deliberately.  A school may state that a diploma and other requirements such as community service and senior projects are required to walk in graduation ceremonies.  This may seem reasonable, but a diploma is not issued until community service and a senior project are accepted.  They are requirements for a diploma, not graduation!  Where is the compelling school need to circumvent state law? In short, applying non-diploma requirements suggests that parents who sue should seek monetary damages from individuals, not just the right to walk from a school or district.

Precedent has been set for letting students not complete requirements in courses, but receive credits and grades of A with a boost in GPA.  It is said that this practice is unofficial, but it is publicly recognized and accepted by administrators, with the caveat that by law teachers have this right in grading. However, these grades are used by the administration in boosting GPA scores that are used in school awards. This makes them official, not just tolerated. This is NOT a gray area as a result, but subjects schools to charges of hypocrisy, which undermines any LEA's arguments on consistency or integrity.  Currently, many teachers award grades in AP courses based solely on AP test results. Classwork and participation are irrelevant.  In short, the AP test is to AP course requirements as the CHSPE test is to high school requirements.  If a school wants to argue that top students deserve special treatment while at-risk students should be treated brusquely . . . lots-of-luck!  It is this argument that two lawyers who have reviewed this blog state would force a judge to rule in favor students. Almost without question, the official GPA boost from faulty AP grades is far more damaging to a school's environment than letting CHSPE students walk. To argue otherwise is obtuse.

Walking in graduation has been denied on behavioral grounds.  For example, getting drunk at grad night disqualifies a student.  Passing CHSPE is a positive event.  In the past, pregnant woman and convicts who have served time, were not allowed to walk.  Now they do, often with strong school and community praise. Is passing CHSPE sui generis? No. On its face, it is simply absurd to deny CHSPE students the opportunity to walk.