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Connected Mathematics

Connected Mathematics is a comprehensive, problem-centered curriculum designed for all students in grades 6-8 based on the NCTM standards. The curriculum was developed by the [|Connected Mathematics Project (CMP)] at Michigan State University and funded by the National Science Foundation.

Each grade level curriculum is a full-year program, and in each of the three grade levels, topics of number, algebra, geometry/measurement, probability and statistics are covered in an increasingly sophisticated manner. The program seeks to make connections within mathematics, between mathematics and other subject areas, and to the real world. The curriculum is divided into units, each of which contains investigations with major problems that the teacher and students explore in class. Extensive problem sets are included for each investigation to help students practice, apply, connect, and extend these understandings.

Connected Mathematics addresses both the content and the process standards of the NCTM. The process standards are: Problem Solving, Reasoning and Proof, Communication, Connections and Representation. For example, in Moving Straight Ahead students construct and interpret concrete, symbolic, graphic, verbal and algorithmic models of quantitative and algebraic relationships, translating information from one model to another.

Like other curricula implementing the NCTM standards, Connected Math has been criticized by supporters of traditional mathematics for not directly teaching standard arithmetic methods.

Research Studies

One 2003 study compared the mathematics achievement of eighth graders in the first three school districts in Missouri to adopt NSF-funded Standards-based middle grades mathematics curriculum materials (MATH Thematics or Connected Mathematics Project) with students who had similar prior mathematics achievement and family income levels from other districts. Significant differences in achievement were identified between students using Standards-based curriculum materials for at least 2 years and students from comparison districts using other curriculum materials. All of the significant differences reflected higher achievement of students using Standards-based materials. Students in each of the three districts using Standards-based materials scored higher in two content areas (data analysis and algebra), and these differences were significant.

Another study compared statewide standardized test scores of fourth-grade students using Everyday Mathematics and eighth-grade students using Connected Mathematics to test scores of demographically similar students using a mix of traditional curricula. Results indicate that students in schools using either of these standards-based programs as their primary mathematics curriculum performed significantly better on the 1999 statewide mathematics test than did students in traditional programs attending matched comparison schools. With minor exceptions, differences in favor of the standards-based programs remained consistent across mathematical strands, question types, and student sub-populations.


As one of many widely adopted curricula developed around the NCTM standards, Connected Mathematics has been criticized by advocates of traditional mathematics as being particularly ineffective and incomplete and praised by various researchers who have noted its benefits in promoting deep understanding of mathematical concepts among students. In a review by critic James Milgram, "the program seems to be very incomplete... it is aimed at underachieving students." He observes that "the students should entirely construct their own knowledge.. standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions." However, studies have shown that students who have used the curriculum have "develop[ed] sophisticated ways of comparing and analyzing data sets, . . . refine[d] problem-solving skills and the ability to distinguish between reasonable and unreasonable solutions to problems involving fractions, . . . exhibit[ed] a deep understanding of how to generalize functions symbolically from patterns of data, . . . [and] exhibited a strong understanding of algebraic concepts and procedures," among other benefits.

Districts in states such as Texas were awarded NSF grants for teacher training to support curricula such as CM. Austin ISD received a $5 million NSF grant for teacher training in 1997. NSF awarded $10 million for "Rural Systemic Initiatives" through West Texas A&M. At the state level, the SSI (Statewide Systemic Initiative), was a federally-funded program developed by the Dana Center at the University of Texas. Its most important work was directing the implementation of CM in schools across the state. But in 1999, Connected Mathematics was rejected by California's revised standards because it was judged at least two years below grade level and it contained numerous errors . After the 2000-2001 academic year, state monies can no longer be used to buy Connected Mathematics

The Christian Science Monitor noted parents in Plano Texas who demanded that their schools drop use of CM, while the New York Times reported parents there rebelled against folding fraction strips rather than using common denominators to add fractions. For the improved second edition, it is stated that "Students should be able to add two fractions quickly by finding a common denominator". The letter to parents states that students are also expected to multiply and divide fractions by standard methods.

What parents often do not understand is that students begin with exploratory methods in order to gain a solid conceptual understanding, but finish by learning the standard procedures, sometimes by discovering them under teacher guidance. Large-scale studies of reform curricula such as Connected Mathematics have shown that students in such programs learn procedural skills to the same level as those in traditional programs, as measured by traditional standardized tests. Students in standards-based programs gain conceptual understanding and problem-solving skills at a higher level than those in traditional programs.

Despite disbelief on the part of parents whose textbooks always contained instruction in mathematical methods, it is claimed that the pedagogical benefits of this approach find strong support in the research: "Over the past three to four decades, a growing body of knowledge from the cognitive sciences has supported the notion that students develop their own understanding from their experiences with mathematics."

Examples of criticism

Connected Mathematics treatment of some topics include exercises which some have criticized as being either "subjective" or "having nothing to do with the mathematical concept" or "omit standard methods such as the" formula for arithmetic mean. (See above for discussion of reasons for initial suppression of formulas.) The following examples are from the student textbooks, which is all the parents see. (See discussion below.)


In the first edition, one booklet focuses on a conceptual understanding of median and mean, using manipulatives. The standard algorithm was not presented. Later editions included the algorithm.

Comparing fractions

In the 6th grade u

Teach For America

Teach For America (TFA) is an Americannon-profit organization that recruits recent college graduates and professionals to teach for two or more years in low-income communities throughout the United States.


The organization was founded by Wendy Kopp, after she developed the idea to help eliminate educational inequity in the United States for her senior thesis at Princeton University in 1989. Since its beginning in 1990, more than 14,000 corps members have completed their commitment to Teach For America. The history of the organization is chronicled in her book "One Day, All Children: The Unlikely Triumph of Teach For America and What I Learned Along the Way"

Applying to Teach For America has become very popular among seniors at some of America's elite colleges. In its first year, Teach For America placed only 500 teachers; in 2007, the organization received more than 18,000 applications resulting in 2,900 new corps members. These applicants included "11 percent of the senior classes at Amherst and Spelman; 10 percent of those at University of Chicago and Duke; and more than eight percent of the graduating seniors at Notre Dame, Princeton and Wellesley.".


Teach For America recruits recent college graduates and professionals to teach for two years in low-income communities throughout the United States. The goal of Teach For America is for its corps members not only to make a short-term impact on their students, but also to become lifelong leaders in pursuing educational equality. Corps members do not have to be certified teachers, although certified teachers may apply.

Uncertified corps members receive alternative certification through coursework taken while completing the program. Corps members attend an intensive five-week summer institute to prepare for their commitment. Teach For America teachers are placed in schools in urban areas such as New York City and Houston, as well as in rural places such as eastern North Carolina and the Mississippi Delta. They then serve for two years and are usually placed in schools with other Teach For America corps members.

Teach For America teachers are full-fledged faculty members at their schools, receiving the normal school district salary and benefits as well as a modest AmeriCorps "education voucher" (which can be used to pay for credentialing courses, cover previous student loans or fund further education after the two-year commitment).

Educational Impact

Since the founding of the organization, several independent studies have been conducted to gauge the effectiveness of Teach For America corps members relative to teachers who entered the teaching profession via other channels. Most recent studies suggest that Teach For America corps members are more effective than new teachers from more traditional certification programs.

In a study published by the Urban Institute and the Calder Center in March 2008, the authors found "that TFA teachers tend to have a positive effect on high school student test scores relative to non-TFA teachers, including those who are certified in-field. Such effects exceed the impact of additional years of experience and are particularly strong in math and science."

Mathematica Policy Research also addressed this question in a study published in June 2004. The study compared the gains in reading and math achievement made by students randomly assigned to Teach For America teachers or other teachers in the same school. The results showed that, on average, students with Teach For America teachers raised their mathematics test scores 0.15 standard deviations more than the gains made by other students. This is equivalent to students having received one extra month of instruction. In reading, students with Teach For America teachers performed similarly to students with other teachers.

According to an independent study by Kane, Parsons and Associates Inc. in 2003, the great majority of principals who work with Teach For America teachers contend that Teach For America corps members make a significant and positive impact in their classrooms. 90% of principals expressed that Teach For America teachers are as well-prepared to teach as other beginning teachers. 66% believed that Teach For America's training is "better than average."


In the past much of the organization's efforts have been tightly focused on recruitment, but are now shifted to boosting the retention rate. Teach For America reports that 34% of their alumni teach at their placement schools for a third year. Many others go on to teach elsewhere, especially at KIPP charter schools and other schools founded by Teach For America alumni. Still others train for administrative positions, and Teach For America now reports that 63% of its alumni are working or studying in education.

Geographical reach

Teach For America's geographical impact has also grown. Originally serving only 6 regions, Teach For America is now active in 39 regions:

Mathematical table

Before calculators were cheap and plentiful, people would use mathematical tables—lists of numbers showing the results of calculation with varying arguments— to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks.

A simple but common example is the multiplication table, which most people know from their early mathematics classes:

To find the result of 7×8, one looks in the left column to seven, then across the "seven-line" to eight. The easily found answer is 56. To find 9×3, one would swap the factors and find the equal product 3×9 (27) by the same technique.

History and use

Tables of trigonometric functions were first known to be made by Hipparchus. Tables of common logarithms and antilogarithms were used to do rapid multiplications, divisions, and exponentiations, including the extraction of nth roots. Tables of special functions are still used. For example, the use of tables of values of the cumulative distribution function of the normal distribution– so-called standard normal tables – remains commonplace today, especially in schools.

Mechanical special-purpose computers known as difference engines were proposed in the 19th century to tabulate polynomial approximations of logarithmic functions – i.e. to compute large logarithmic tables. This was motivated mainly by errors in logarithmic tables made by the human 'computers' of the time. Early digital computers were developed during World War II in part to produce specialized mathematical tables for aiming artillery. From 1972 onwards, with the launch and growing use of scientific calculators, most mathematical tables went out of use.

Creating tables is a common code optimization technique, and works as well for computers as humans. In computers, use of such tables is done in order to speed up calculations in those cases where a table lookup is faster than the corresponding calculations (particularly if the computer in question doesn't have a hardware implementation of the calculations). In essence, one trades computing speed for the computer memory space required to store the tables.

Tables of logarithms

A major type of mathematical tables are tables containing logarithms. Prior to the advent of computers and calculators, using logarithms meant using such tables, which were mostly created manually. Base-10 logarithms are useful in computations when electronic means are not available. See common logarithm for details, including the use of characteristics and mantissas of common (i.e., base-10) logarithms.

In 1617, Henry Briggs published the first installment of his own table of common logarithms, containing the logarithms of all integers below 1000 to eight decimal places. This he followed, in 1624, by his Arithmetica Logarithmica, containing the logarithms of all integers from 1 to 20,000 and from 90,000 to 100,000 to fourteen places of decimals, together with a learned introduction, in which the theory and use of logarithms are fully developed. The interval from 20,000 to 90,000 was filled up by Adriaan Vlacq, a Dutch mathematician; but in his table, which appeared in 1628, the logarithms were given to only ten places of decimals.

Vlacq's table was later found to contain 603 errors, but "this cannot be regarded as a great number, when it is considered that the table was the result of an original calculation, and that more than 2,100,000 printed figures are liable to error." An edition of Vlacq's work, containing many corrections, was issued at Leipzig in 1794 under the title Thesaurus Logarithmorum Completus by Jurij Vega.

François Callet's seven-place table (Paris, 1795), instead of stopping at 100,000, gave the eight-place logarithms of the numbers between 100,000 and 108,000, in order to diminish the errors of interpolation, which were greatest in the early part of the table; and this addition was generally included in seven-place tables. The only important published extension of Vlacq's table was made by Mr. Sang in 1871, whose table contained the seven-place logarithms of all numbers below 200,000.

Briggs and Vlacq also published original tables of the logarithms of the trigonometric functions.

Besides the tables mentioned above, a great collection, called Tables du Cadastre, was constructed under the direction of Gaspard de Prony, by an original computation, under the auspices of the French republican government of the 1790s. This work, which contained the logarithms of all numbers up to 100,000 to nineteen places, and of the numbers between 100,000 and 200,000 to twenty-four places, exists only in manuscript, "in seventeen enormous folios," at the Observatory of Paris. It was begun in 1792; and "the whole of the calculations, which to secure greater accuracy were performed in duplicate, and the two manuscripts subsequently collated with care, were completed in the short space of two years." CubicFrom Yahoo Answers

Question:Any websites that are free that teach Algebra 1? I haven't taken any Algebra classes yet, but I want to learn it over the summer so I can get ahead. 2 weeks of school left and I've taken Pre-algebra so far. They are pretty good of what I have seen. I have looked up a couple things on there in the past and it explains them well. If you can, ask your teacher if you can borrow a Algebra 1 book for the summer. That's what I did for Algebra 2. I HIGHLY recommend that you know ->100%<- of Algebra 1 before skipping it. You will need every bit of it!

Question:Like how colleges have online schools, are Jr. High and high school taught online?

Answers:Yes, check out Depending on what state you live in, High School may be offered through the free online school.

Question:I'm currently enrolled in an online course through my community college, which consists of weekly discussions, quizzes, and a final. At first the Professor seemed great, involving herself in our interpretations of the chapter and all that stuff. However, after the second week (we are in our 7th) she has been completely absent. After taking three quizzes and realizing they were not added in the gradebook, I emailed the Professor regarding this and recieved no response. Then today I find she has updated all the discussion to date (she only had the first week before) and its looks as though she just gave me whatever came to her mind as a grade. 12/15, 10/15, 14/15. Which is strange because the syllabus just said to respond to the question and respond to someone else. Which I do, and always include plenty of info. This Professor is acting totally unprofessional here. I realize it's an online class, but I have sent her two emails that have gone almost 2 months with no response. I feel I should report her to the school. I don't want to, but she is messing with my grade and giving no reason because shes "MIA," Any ideas on how to handle this situation? Thank you. I'm not sure I made it clear enough in the question, but she recently came back to put grades in on sporadic assignments, but then vanished again. Basically shes like a phantom teacher. I was also going to ask that if I were to submit an inquiry to an administrator asking where she is and she gets chastized by the administration, that could possibly affect me, right? Even if i'm annonymous she will know I was the one (hopefull there were more) sending the emails and she might be biased against me.

Answers:This is the professors job, and it seems like she is not doing a great job at it. If she is not responding to your emails, chances are she is not responding to others. I would not be surprised if others have complained already. If i was in that situation, I would go directly to the dean. You have paid for the class, so you should be learning and have a supportive professor. You should be able to look at the syllabus and see where all the points are coming from. Those points combined make up your finally grade. If it turns out things are being changed, that will be another thing to bring up to the dean. Did it state on the syllabus that these particular grades would be counted in your final grade? This should not effect you at all...someone who is not doing their job should get called out. If this teacher becomes bias against you..They are NOT in the right profession!!! You would also have the right to file a complaint. Go Hawks!!

Question:Hello. I want to great a good website to teach mathematics. Now, I dont live in United States, so I don't know what subjects we learn each grade. Could you tell me what exactly, you learn in Grade 8 in High School? If possible, please write me in order. If you want FREE GMail Invites, just write your e-mail down your answer to my question and I will be glad to give you an invite for helping me out here. Thank you all.

Answers:The majority of the 8th graders here are doing Algebra I as well, but Pre-Algebra and Geometry are also classes that 8th graders are taking.

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