By Stuart Singer, The Teacher Leader

The key to creating an illusion is to distract the viewer.  Draw the attention away from the sleight of hand and the audience will believe they have seen magic.  Apparently this technique is now a key element when dealing with the analysis of standardized test results.  The plan appears to be to use some new and often outrageous assertion to distract the public and “abracadabra” many of the problems inherent in the No Child Left Behind (NCLB) and end-of-course standardized testing magically disappear. 

The latest form of deception is an idea being floated by educational leaders in Virginia.  They are considering a proclamation announcing that a “pass advanced” on the state’s Standards of Learning (SOL) exams is an indication of college preparation.  The word “advanced” in most contexts indicates a significant level of accomplishment; in this case, however, it should not be confused with readiness for post high school study. 

It is actually more of a numbers game

At first glance a “pass advanced” might appear to be a significant achievement.  It requires a score of 500 or more on a test scaled to go from 200-600 (400 is required for passing).  But as in other forms of magic, these numbers are an illusion.  Like many other end-of-course exams being used for NCLB, the SOL is a four-option multiple-choice test with no penalties for wrong answers.  Consequently the actual range of scores is not nearly as large.  The laws of probability decree anyone answering 50 such questions would start with 12 or 13 correct responses simply by random guessing.  In 2011 a passing score of 400 on the Algebra 1 exam required 23 correct answers.   As a result of that scale, every student begins with a score of at least 340.  Thus the real possible range is 340-600.  Suddenly a tally of 500 does not seem quite so “advanced”. 

Forty-four correct answers will earn a student a 500.   Even if this were an exam with open-ended questions and penalties for wrong responses, mastery of only 88% of the curriculum is hardly college-level work.   But with a multiple-choice, no penalty format, 44 accurate responses represent much less.  A few quick calculations reveal that if a student can answer 42 questions, probability will produce the missing two from the remaining eight.  Now the mastery level is down to 84%--a “B-“on most grading scales.  Even those numbers are a bit skewed.  If an individual can eliminate one or two potential answers in a question the likelihood of a successful “guess” increases exponentially. 

Adding to these misperceptions is the limited nature of such forms of questions.  They cannot require multiple-step responses or demand a true demonstration of mastery of the most complex or intricate aspects of a subject.  They can only ask questions that have reasonably simple answers.  It quickly becomes clear that based on almost any analysis, a pass “advanced” on these tests is not a predictor of college success. 

To get quality, you need quality

As Mel Riddile discussed in a previous post, tests made on the cheap are susceptible to both cheating and inflated results.   If Virginia and other states want to administer tests that are indicators of future educational success, they will need to move away from the current easy-to-grade and inexpensive formats and invest in exams that will accurately measure a student’s mastery of a class.  Until then, any claim of academic prowess based on the results is nothing more than an illusion and distraction.

Posted by Mel Riddile at 06:41 AM | Permalink

by Stuart Singer, The Teacher Leader

There are few lightning rods in the educational landscape of 2011 that rival the debate on the role of testing in the evaluation of student, teacher and school performance.  However, another perspective on this topic was addressed in a recent Mel Riddile post which discussed research indicating that frequent testing had a positive impact on learning.

According to Dr. Riddile, “A recent study summarized in Science magazine and reported in a New York Times article titled To Really Learn, Quit Studying and Take a Test may be a key to unlocking some keys to the teaching and learning process.”  This discussion does not concern the end-of-course barrier exams that are the focal point of most educational conversations.  The research revolves around the use of testing within a teacher’s daily lesson planning.  The study found “practicing retrieval produces greater gains in meaningful learning than elaborate studying.”  As Dr. Riddile notes, “In other words, the simple act of taking a test may improve learning better than any other studying technique including note taking and concept mapping.”

Perhaps the most compelling conclusion noted revolved around the retention of information.  “The Times article went on to say, The research, published online Thursday in the journal Science, found that students who read a passage, then took a test asking them to recall what they had read, retained about 50 percent more of the information a week later than students who used two other methods. One of those methods — repeatedly studying the material — is familiar to legions of students who cram before exams. The other — having students draw detailed diagrams documenting what they are learning — is prized by many teachers because it forces students to make connections among facts.”

The view from the classroom

For forty years I taught high school mathematics.  For the last thirty-eight I employed a teaching technique that paralleled the views expressed in those studies.  Whether the subject was General Math, Algebra 1, Algebra 2 or Pre-calculus I created a classroom strategy that was clearly focused on the concept of frequent and consistent testing.   It was a plan that was simple and direct. 

The centerpiece of the plan

Every class period included a quiz.  It always contained relatively simple questions that could be completed in ten to fifteen minutes.  Questions would be graded on a “right or wrong” basis with little partial credit involved.  It would be the math equivalent of a short-answer, fill-in-the-blanks question.  As the previously noted research found, the regular testing of information led to a number of extremely important outcomes.  Not only did the students retain the material better, they were also clearly aware of their academic status in the class.   A daily evaluation of one’s performance means no one is surprised by their ultimate success or failure.  The teacher also benefits from having a barometer of student learning in every class period.   A quiz that results in a significant number of poor grades requires more work on the topic.  One that indicates overall comprehension allows an educator to move forward with confidence.  Since it is critical that these papers be returned the next class meeting, they must be easy to grade.  The best utilization of time for the teacher is to be able to grade one set of papers while the next class is taking their quiz. 

A systematic approach

My overall classroom strategy was to introduce every topic in three consecutive classes.  The daily quiz was a key component of that plan.  This approach was used regardless of the level of the math or whether the school utilized a block or non-block schedule.  On day 1 a topic would be presented to the students.  An explanation of the concept would be followed by examples and then homework would be assigned to give the students practice.  Day 2 would begin with a review of the homework.  After that review was completed and all questions were answered, a quiz would be given.  Designed to cover this one concept, it was based on questions similar to those found on the homework.  On day 3 the quiz would be returned and reviewed.  

This philosophy was explained in detail to the students on the first day of school.  A typical class would be divided into four segments.  Part one was returning the quiz from the previous session and discussing any questions.  The next segment was reviewing the homework assignment.  Often a worksheet would follow to ensure understanding.  At the conclusion of that conversation the class was given a quiz.  The fourth and final element of the period was devoted to the next topic which would be then practiced in a homework assignment. The next class would be structured in the same manner.   By following this schedule every topic was discussed in three consecutive classes.

It sounds so boring

Obviously, such a highly-structured approach could be a formula for boredom.  Though the basic plan never changed, the challenge for the teacher was to create variety within the segments.  On some occasions I would have my “A” students write the quiz solutions on the board.  An “A” student was anyone who received a grade of “A” on that particular quiz.  Students quickly perceived this opportunity as an “honor” and since all students at one time or another would have a perfect paper I would take care throughout the year to have as many different students as possible receive this recognition.  It was stunning to watch otherwise sophisticated 18-year-olds become giddy when they had a chance to demonstrate their math prowess.  On other occasions, I would personally focus on any problem that was missed by a significant number of students. 

The review of the homework was also approached in different ways.  Volunteers would be solicited on some occasions; other times students were assigned problems.  A third option would have me do the work.  The practice worksheets could be presented as individual work, group projects, contests, or puzzles.  The outcome was always the same—practice—but the methods would vary from day to day. 

The introduction of the new topic would also be open to a variety of educational strategies.  Lecture, group discovery, question-answer and any other method available would be employed on different occasions.

Students love structure

People are most comfortable when they have a familiar routine.  When students feel comfortable in a class they become more confident.  By the end of the first week of school, my students understood the process and knew what to expect each day.  There were no surprises.   At the end of every year I would give my students the opportunity to complete an anonymous evaluation of the course.  When asked for the aspect that contributed the most to their success, the daily quiz was selected more often than all of the other options combined. 

The sincerest form of flattery

Over the course of my career a number of teachers adopted my “daily quiz” approach to teaching.  These individuals taught in courses all across the curriculum.  Many reported not only improved learning but also better communication in terms of student performance.  My wife, an associate Biology professor at a junior college, has successfully used the same strategy with her students. 

Clearly from my perspective those research studies are truly on to something.

Posted by Mel Riddile at 11:28 AM | Permalink

by Stuart Singer, The Teacher Leader

Recently the Washington Post ran an article featuring a high school sponsored poker club.  The article appeared to support the idea that poker clubs were a legitimate way to help students learn mathematical concepts. Although using the structure of poker to create a lesson in probability is a valid and effective technique; creating a club that is dedicated to playing poker and then claiming that it is academically suitable demonstrates extremely poor judgment on the part of the adults involved.     

Teaching the wrong things

When asked about the group, the principal of the school gave his support to the concept.  He told the Post:   

“We know the kids could play outside of school, but when they're here, we have the opportunity to show them how to play responsibly and to show them how the game relates to their education.”

While the rules of poker are based in large part on the laws of probability, teaching students how to play the game has far more to do with gambling than mathematics.  It was clear that the “math first” message was becoming obscured when posters advertising the club featuring pictures of poker playing dogs smoking cigarettes began to appear in the building.  The principal ordered them torn down.   This gesture eliminated the pictures but not the inherent problem.  

A very good teaching tool

When I taught probability to my pre-calculus students I regularly used poker hands as a portion of my lessons.  The standard deck of playing cards with its 13 different values, four suits and two colors presents unlimited possibilities for constructing problems and illustrations.  One of the classroom activities consisted of dividing the students into small groups to determine the probability of seven specific five-card poker hands.  After mathematically computing their answers, the results would be compared and the method for computing the correct probabilities was demonstrated.  The concluding activity was to rank the value of the hands correlated to the diminishing probability of their occurrence.  It was then determined that this student-created listing was exactly the same as the actual rules of the game.Instead of pulling out the poker chips after this worksheet was completed, the next step was to expand the understanding of the probability involved.  For example, it had been previously determined that the likelihood of having five cards and no matches was 50.7%; the chance that there would be one match was 42.3%.  It was now time to turn the process upside down.  If a person was given fourteen cards what were the chances of no matches?  The answer, of course, is zero since there are only thirteen different values. The follow up problem was how many cards must be dealt in order for it to be more likely to have a pair than to have no matches?”  (The answer is seven.  Variations of this question were given on the chapter test.)

While there were lengthy conversations about playing cards in my classes no deck was ever in the room.   We did not talk about any strategies for playing these games and most certainly would not encourage anyone to do so. The major point of emphasis was the purity of the mathematics involved. Because of their precision, these numbers have withstood the test of time in a game that has centuries of history. 

Sending the wrong message

Poker clubs designed with the alleged intent of teaching mathematics are found at colleges around the country.  The idea began at Harvard Law School.  There are, however, vast differences between the reasoning abilities of graduate students and those of high school students.  The high school math teacher who hosts the aforementioned club in his classroom speaks to the age difference, “The older kids realize that it's about odds and probability," he says, "the younger ones just want to win.”

High stakes gambling on poker has been glamorized on television and on the Internet.  Having teenagers play this game of chance and giving them any indication that they are becoming mathematically equipped to control outcomes is not only incorrect but potentially dangerous. 

Should educators be concerned about youth gambling?

The following are some conclusions from a study of 1000 randomly selected adolescents 13-17 years old by the Oregon Gambling Addiction Treatment Foundation.   (Carlson & Moore, 1998)

• Seventy-five percent of teens in the study reported having gambled.
• One in ten teens was an at-risk gambler.
• Rates of problem gambling among youth were 2 to 4 times higher than the rates for adult gambling.
• Youth can hide gambling problems well.  There are no outward, physical signs.

The article in the Washington Post quoted one seventeen-year-old who had a large pile of chips in front of him as saying, “I don't know whether math class is helping me with poker, or whether poker is helping me with math.”  A very good question that I am not sure the adults at his school can answer.   

Posted by Mel Riddile at 02:37 PM | Permalink

I hesitate to address the sensitive topic of international comparisons with school leaders who have to face the reality of leading schools on a day-to-day basis. However, I wasn't subjected to the kind of attacks on public schools, teachers, and principals that we have experienced of the past year. In the past, when NAEP or PISA results were released, we simply shrugged our shoulders and moved on. Today, however, our teachers and community expect us to respond when asked. In fact, our silence on this matter could be deafening.

That is why I put together some talking points for school leaders on the 2009 PISA results. I have drawn from a number of sources including the Organization for Economic Cooperation (OECD), which coordinates the international assessments and the Washington Post.

Background

• Begun in 2000, the Program for International Student Assessment (PISA) is a system of international assessments that focuses on 15-year-olds' capabilities in reading literacy, mathematics literacy, and science literacy.
• PISA is coordinated by the Organization for Economic Cooperation and Development (OECD), an intergovernmental organization of industrialized countries. 38 OECD nations and 28 partner nations participated in the assessment.
• PISA includes measures of general or cross-curricular competencies such as problem solving.
• PISA emphasizes functional skills that students have acquired as they near the end of compulsory schooling.
• The U.S. sample for the latest results includes both public and private schools, with 165 schools and 5,233 students participating in all. Schools are randomly selected and 15-year-old students within those schools are randomly selected.

2009 Results

• Reading: The U.S. average score in reading (500) was not measurably different than other OECD countries. U.S. female students scored higher than male students.
• U.S. 15-year-olds had an average score of 500 on the combined reading literacy scale, not measurably different from the OECD average score of 493. Among the 33 other OECD countries, 6 countries had higher average scores than the United States, 13 had lower average scores, and 14 had average scores not measurably different from the U.S. average. Among the 64 other OECD countries, non-OECD countries and other education systems, 9 had higher average scores than the United States, 39 had lower average scores, and 16 had average scores not measurably different from the U.S. average. 

• Math: U.S. average score in math was lower than the OECD average. Male students, in general, scored higher than female students. Since 2006, U.S. has caught up with 9 countries.
• U.S. 15-year-olds had an average score of 487 on the mathematics literacy scale, which was lower than the OECD average score of 496. Among the 33 other OECD countries, 17 countries had higher average scores than the United States, 5 had lower average scores, and 11 had average scores not measurably different from the U.S. average. Among the 64 other OECD countries, non-OECD countries, and other education systems, 23 had higher average scores than the United States, 29 had lower average scores, and 12 had average scores not measurably different from the U.S. average score. 

• Science: 12 other OECD countries had higher average scores than the United States.
• On the science literacy scale, the average score of U.S. students (502) was not measurably different from the OECD average (501). Among the 33 other OECD countries, 12 had higher average scores than the United States, 9 had lower average scores, and 12 had average scores that were not measurably different. Among the 64 other OECD countries, non-OECD countries, and other education systems, 18 had higher average scores, 33 had lower average scores, and 13 had average scores that were not measurably different from the U.S. average score.
• Male students scored higher than female students. Overall score was higher than 2006, and the gains in science exceeded those for math.
• The US is one of three nations that give more money to highly advantaged schools than to disadvantaged schools.
• Overall, private schools do better on PISA...until you account for SES.
• There are number of high performing economically disadvantaged schools in the US: "success is possible against all odds."

U.S. Strengths and Weaknesses

• U.S. students showed the best relative performance in answering questions that judged students’ ability to reflect and evaluate information. On that measure, the United States ranked seventh out of the 34 OECD nations.
• The weakest area for U.S. achievement was in accessing and retrieving information, for which students tied for 19th place with France.

Behind the Facts

• The PISA rankings are determined by nations’ average scores. "Some researchers have suggested, however, that average score comparisons are not useful: even presuming that the tests have some meaning for future accomplishment, average students are not likely to be the leaders in fields of mathematics and science."
• In the last administration of PISA, the United States has 25% of all high-scoring students in the world. Among nations with high average scores, Japan accounted for 13% of the highest scorers, Korea 5%, Taipei 3%, Finland 1%, and Hong Kong 1%.
• The fact that one of four high-scoring students came from the United States and the remaining high-scores came from the other 58 countries participating "suggests that many American schools are actually doing very well indeed."
• "Well-resourced schools serving wealthy neighborhoods are showing excellent results. Poorly resourced schools serving low-income communities of color do far worse."
• The U.S. had many more students scoring at the lowest levels; these kids likely can’t compete for the good jobs in the country."
• "Americans in low-poverty schools look very good, even in mathematics. They would be ranked third in the 4th grade (among 36 nations) 6th in the 8th grade (among 47 nations). This is important because while other developed nations have poor children, the U. S. has a much higher proportion and a much weaker safety net. When UNICEF studied poverty in 22 wealthy nations, the U. S. ranked 21st."
• The highest scoring countries have less diversity and less poverty.

PISA confirms what we already know. The U.S. is quite capable of producing top performing students in well-resourced schools serving middle class neighborhoods. Under-resourced schools in poor neighborhoods do not fare as well.

Resources:

OECD

Are today’s students prepared for the knowledge economy of the 21st century?

PISA: Who made the grade? (OECD)

Washington Post

Do international test comparisons make sense?

Hysteria over PISA misses the point

Posted by Mel Riddile at 11:54 AM | Permalink

The Teacher Leader just threw more gasoline on the fire. Algebra for all students in grade 8 is a hot topic that will only get hotter. The recent studies that cite Algebra I success in eighth grade as a predictor of college success will only fan the flames of controversy pitting policy makers who want to say that they are raising standards against teachers who want students to actually learn something.

I have some thoughts on the subject for school leaders:

One Size Fits All

Anytime someone in education suggests one approach for all students, I get very nervous. The very same people who want teachers to differentiate instruction in classrooms are the same people who refuse to differentiate their approach to district policy. Years ago, a district leader had the bright idea of eliminating earth science from the high school curriculum because the top university in the state did not consider earth science to be a laboratory course. Instead, all ninth graders would be required to take Biology. Previously, about 60-70% of all ninth graders took Biology, and of course, it was the top students. The logic here escapes me. We were going to suddenly raise the college readiness levels of 30-40% of our students, not by improving student literacy and math skills, but by not teaching earth science. This bright idea eliminated the jobs of hundreds of science teachers, increased the failure rate in Biology dramatically, and did nothing to improve college readiness. Incidentally, the timing was impeccable. Just as the environmental movement was gaining momentum, this school district eliminated the study of the environment. How’s that for meaningful and relevant?

Hurry Up and Learn

We are in such a hurry to accelerate students that we forget to ensure that they actually learn something. One school system insisted that all tenth graders take Chemistry. As an aside, I seem to recall that the U.S. approach to math had been criticized for a breadth over depth philosophy. For a decade the district staff harassed and criticized the Chemistry teachers, who insisted that students needed a solid algebra foundation in order to succeed in Chemistry. District staff believed that the Chemistry teachers were excusing their lack of pedagogical skills until they actually looked at the numbers. Thirty days after a fist-pounding tirade in a Chemistry teacher in-service program in which district staff said, “We are going to raise our Chemistry scores, and don’t tell me it’s the math,” the same people sat before thirty high school principals directing them to take all students who had not completed Algebra I with a C our better out of Chemistry. Why? “Because our analysis indicates that they will all fail the state test. That’s why.” Finally, someone had listened to the teachers. Of course, these people would never admit that they were wrong and that the teachers had been right all along. Nor, would they acknowledge the thousands of students who had been forced down the school district’s conveyor belt so that district staff could brag to their colleagues at national conferences “all of our 10^th graders take Chemistry.”

The Best or the Best Prepared

Without an aligned math curriculum that is designed to prepare students from K-7 to successfully master Algebra I in the eighth grade, all we are really doing is identifying the brightest students not the best prepared.

Screen Them Out or Raise Them Up

I was just talking with a friend who lamented that her high school English teacher did not recommend her for AP English and that she was forced to sit in classes in which a majority of the students were not highly motivated. This individual went on to attend and graduate from a competitive, four-year college. I will admit that I have a problem with arrogant elitists who believe that it is their responsibility to sort the capable from the less capable. This fixed mindset—the belief that talent and intelligence are inherited and that one either has it or does not have it--has and is causing serious damage in our schools and wasting talent that we cannot afford to waste. We need to develop a growth mindset in our teachers and staff—the belief that work and effort create ability and that success is the result of persistent, correct, and deliberate practice.

What Colleges Really Want – School leaders get mixed messages from colleges and universities. I have had two deans of prestigious engineering schools tell me that they did not want students to take Calculus in high school. They merely wanted the incoming students to have a solid foundation in Algebra. This made it clear to me that the admissions officials were not talking with their own faculty. So, here I am trying to get my students to take higher-level math and the colleges are telling them that it is not important. The only problem is that the admissions people demand more AP and IB courses and a more rigorous course of study as a condition for admission.

The Bottom Line

I spent an entire year of my life promoting the idea that our school system needed to double the number of 8th graders taking Algebra I. I want more and more 8th graders prepared to successfully master Algebra I. Notice that I said, “successfully master.” I have been through too many of these “up the ante” initiatives over the years that simply force more students into higher-level courses with no effort made to improve the preparation of the students. Then, when the failure rate increases dramatically, they blame the teachers. If we don’t care if our students learning anything, we can simply declare, like many districts have done, that more 8thgraders will take Algebra I. The truth is that more 8th graders successfully mastering Algebra I will not be accomplished by edict. It will take a lot of work and effort to align the curriculum and to properly train teachers in grades K-7. All students can achieve to high levels if they are given enough time and the proper preparation.

Posted by Mel Riddile at 02:59 PM | Permalink

by Stuart Singer, The Teacher Leader

The quest for improving student performance in mathematics often appears to be something akin to a circular tug-of-war.  If A does not work then try B.  When B flames out it is on to C.  And so it goes until the newest idea is something called A.  There have been so many different formats for Algebra 1 over the past few decades it is beginning to rival the Star Trek franchise for sequels.  The latest batch of bad news concerning math students in the United States compared to their peers around the world has brought on another set of “new” approaches. One of the most popular and potentially counter-productive is the concept of “Algebra 1 for all 8^th graders”.  The premise is simple—if our students are struggling with math and this course is so critical why not have everyone learn it earlier in their scholastic careers.   Here’s my shout to middle school math teachers, “Ready or not, here they come!”  I have to admit the logic escapes me.

But the importance of success in Algebra 1 cannot be underestimated.  Recent studies by Montgomery County Public Schools (MD) have shown a strong correlation between the work done by students in Algebra 1 and Algebra 2 and their ability to obtain a college degree.  Consequently, it is critical when dramatic adjustments are made to the presentation of Algebra 1 that these adaptations result in improved student performance.

Looking at the Data

One of the strengths of standardized testing is, for lack of a better word, the fact that it is standardized.  While classroom grades can be wildly subjective, the results on the same multiple-choice exam given at the same point in the school year graded by the same individuals are not subject to such fluctuations.  In May, 2006 the students taking Honors Algebra 1 in the middle school that feeds into my high school had an average score of 472 on the Virginia Standards of Learning Exam. (The range of scores were from 200-600 with 400 considered passing.) Meanwhile, at the high school, the students taking regular Algebra 1 in grade 9 or later averaged 469 on the exact same test.  At first glance these strikingly similar scores would not seem to be a reason for concern.  One must, however, consider the relative nature of the two groups being tested.  At that time the individuals enrolled in the middle school honors classes were designated as students who were among the top 50% of the class in terms of math skills.  The lower half of the eighth-grade student body, math-wise, was placed into a pre-algebra course and then took Algebra 1 in the ninth grade or later.  When examined under these circumstances the fact that the results for both groups were virtually the same is disturbing for a number of reasons.  When similar comparisons were made between the Honors Geometry and Algebra 2 classes versus the corresponding regular Geometry and Algebra 2 the results showed more than a 50 point advantage to the honors classes.  In addition, a deeper exploration of the actual scores in Algebra 1 shows that an argument could be made that the honors group had poorer results than their regular counterparts.  Not surprisingly among all tested students the vast majority of the highest scores on the Algebra 1 exam were in the eighth-grade group.  These top-heavy results skew the average for this group higher.  The median or middle score for the high school Algebra 1 students was actually higher than the middle school.  When calculating the success of the bottom half of both groups, the “honors” classes performed at a significantly lower level.  As previously stated such results were not duplicated in the other math courses.

Finding the Problem

So what do all of these numerical gymnastics indicate? Does the blame for the shortcomings fall at the feet of the middle school teachers?  Are the testing procedures different in the high school?  Do high school teachers teach more to the test?  The answer to these questions is not a simple A, B or C or even “none of the above”.  The source of most of these poor performances is that too many of these young students were not ready to master the curriculum found in a legitimate Algebra 1 course.  The word “honors” is misplaced in front of Algebra 1 at the middle school in too many instances.  More importantly, these students then enter Geometry and Algebra 2 classes (honors or otherwise) with inferior skills and diminished potential compared to many of the students who took “regular” Algebra 1 in later years.  A letter to the Washington Post from a parent accurately described the plight of these students—they are destined to struggle in math and eventually grow to dislike the subject entirely.  These same results were observed by many of the classroom teachers working with these students in later math courses.  And the negatives are not necessarily limited to the math classroom.  For many adolescents such adverse results in math can spill over into their other subjects as well.  Just as in athletics, in school work, especially sequential topics, success begets success and sadly, failure can bring forth more failure.

Over the next two years the comparison between statistics of the two Algebra 1 groups became more discouraging as the percentage of students being placed early in Algebra 1 continued to increase. Is it any surprise that many high school math teachers are deeply concerned with what will happen when the pool of early Algebra 1 students is mandated to expand to 80% or more?

(Next:  Algebra 1 Is Good for Everyone but Not Every 8^th Grader)

Posted by Mel Riddile at 10:11 AM | Permalink | Comments (1)