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Math

From Bob Dixon and Classical Learning Universe

Math is more than arithmetic...as any 3rd grader facing a challenging state assessment will tell you. Preparing students to think mathematically requires more than addition, subtraction, multiplication, or division...it requires UNDERSTANDING what a given problem is asking and ACTING on that information.

To give students the tools to UNDERSTAND what they're expected to do, Classical Learning Universe developed MATH SUCCESS...a supplemental math problem solving curriculum that teaches students READING COMPREHENSION STRATEGIES FOR MATH PROBLEM SOLVING. This novel, effective program gives students the knowledge and skills they need to effectively solve most problem-solving tasks in their math class as well as on their state assessments.

What is Math Success?

Math Success: Addition and Subtraction and Math Success: Multiplication and Division are forty-lesson math problem solving programs designed to supplement to your regular math program.

Who is it for?

Math Success is designed for students of any age who have mastered addition and subtraction or multiplication and division computations, but who struggle with problem-solving exercises.

How do I use the Math Success program?

Although some teachers might use Math Success in place of some activities from their regular math program, we have designed it as a math supplement. Lessons take approximately fifteen to twenty minutes each.

Lessons can be taught daily, or three times a week. We recommend scheduling the lessons to ensure that students finish Math Success before any spring testing in math.

What is unique about Math Success?

Even students who can perform straightforward computations with ease often struggle when presented with word or story problems. Math Success overtly and thoroughly teaches students how to successfully complete such challenging word problems. Math Success corresponds to the difficulty of math computation frequently assessed in national and state math assessments.

What is taught in Math Success: Addition and Subtraction?

The principal math outcomes of Math Success: Addition and Subtraction are as follows:

Word Attack: Reading Math Words Aloud. Students learn to recognize, read, and understand words used often in math word problems.

Vocabulary. Students learn math vocabulary. In addition, students learn that there are several different phrases math word problems use to ask the same thing (i.e., “take away” and “subtract”).

Words to Problems. Students learn how to read a math word problem and translate the words into a written problem with numbers and symbols.
Matching Number Words and Numerals. Students learn to recognize numbers both by the words that represent them, and by the numerals that represent them.

Paraphrase. Students learn to recognize that the same math problem can be phrased in several different ways, but that all the phrases represent the same computation.

Categories. Students learn that some things can be grouped together into categories and that knowing the categories to which things belong can help in setting up or solving a math word problem.

Words “Understood.” Students learn that math word problems occasionally omit words that are “understood” to be part of the problem. Students learn to recognize these incidences, and to (mentally or in writing) add any omitted words when solving such problems.

Labeling Problem Parts. When presented with a math word problem, students learn to determine which information is given in the problem, and which information is missing or has to be solved for.
More and Fewer. Students learn that problems about “more than” or “fewer than” are subtraction problems. Students also learn how to set up and solve “more than” and “fewer than” math word problems.

What is taught in Math Success: Multiplication and Division?

The principal math outcomes of Math Success: Multiplication and Division are as follows:

Word Attack: Reading Math Words Aloud. Students learn to recognize, read, and understand words used often in math word problems.

Vocabulary. Students learn high frequency math vocabulary. In addition, students learn that there are several different phrases math word problems use to state the same thing (i.e., “divided by” and “goes into”).
Paraphrase. Students learn to recognize alternative ways in which a given problem can be stated.

Words to Problems. Students first learn how to read a simple math problem stated in words, such as “three times six is how many.” They then translate the words into a numerical problem

Graphics to Problems. Students look at groups of items and use them as the basis for doing multiplication and division computations. For instance, a graphic might show three circles with five hearts in each circle. Students multiply to see how many hearts there are total, or divide to find the number of hearts in each group. This illustrates the nature of a substantial number of multiplication and division problem types, and is also the beginning of labeling numbers in problem setups.

Words to Problems - Labeling. Students learn to label identified numbers in word problems, following up their previous work with labeling parts of graphics in problems.

Words and Graphics to Problems. In this activity, students are given problems expressed both as graphics and in words, in order to ensure that they can translate the graphics problems they’ve been doing to word problems.

Making Graphics. Students are often told that a general strategy for solving word problems is to “draw a picture.” Many students are not adept at drawing, and many more don’t know what to draw. This activity is a narrow application of the “draw a picture” strategy, one that students can do and understand.

Words, Graphics, and Pictures to Problems. Problems are presented with words, as well as accompanying graphics or pictures. This is a common way of presenting problems in several standardized tests. As students progress, they do more word problems without pictures or graphics, until Lesson 40, where all the problems are word problems without any illustrations.

What makes Math Success so effective?

Addition and Subtraction Module
Multiplication and Division Module

WHAT MAKES MATH SUCCESS SO EFFECTIVE?

HOW DO I PLACE STUDENTS IN MATH SUCCESS?

Addition and Subtraction Module
Multiplication and Division Module


COMPONENTS AND PRICING

MS Add-sub Websample

MS Mult-div Websample

 

The design of the program is based upon scientifically proven components of instruction shown to be effective for a broad range of students. Briefly, those components include:

Explicit strategy instruction. Any “secrets” of solving math word problems are shared overtly with students. Strategies are neither too narrow nor too broad: they are “intermediate in generalizability” (Prawatt, 1989). The strategies, therefore, are effective for the vast majority of students, especially those students who are unlikely to be able to figure out sophisticated math strategies on their own.


Scaffolding. Students are supported as they learn new strategies, using a variety of techniques. Most strategies are initially laid out step-by-step. Teachers are prompted to help students considerably as students learn new strategies, and exercises prompt students liberally when they first learn new strategies. Gradually, over many lessons, the scaffolding is removed, leading students to apply the strategies covertly, automatically, and independently (Pressley et al., 1989).
Review. The program reviews every targeted outcome continuously. No topic is introduced, practiced, and then suddenly dropped from the program. All topics are reviewed daily for several lessons, and then approximately once every other day thereafter.

Review is distributed, cumulative, and perhaps most critically, varied (Dempster, 1991), and review occurs often enough to ensure mastery of concepts. The variety of practice students experience in Math Success ensures broad generalization and transference to many types and lengths of math word problems, as well as to many types of assessment or other math tasks that students are likely to encounter.
All three of these critical features of effective instructional design are embodied in a sequencing method called “track sequencing.” The opposite of track sequencing is the more familiar “unit sequencing.” In unit sequencing, a given topic is taught for a fixed period of time (such as a lesson, a group of five lessons, a chapter, or some other fixed unit). When the unit is finished, the topic is essentially dropped from instruction.

In the track sequencing of Math Success, students are taught each topic gradually, over many, many lessons. Explicit strategies are taught at the beginning of each track. Each track focuses on just one aspect of math problem solving (e.g., “words to problems”). There is a great deal of scaffolding at the beginning of a track. The scaffolding is gradually reduced over the course of many lessons until finally students are able to successfully apply their strategies independently. It would be difficult, if not impossible, to incorporate explicit strategy instruction, gradually reduced scaffolding, and extensive review into any other method of sequencing than track sequencing.

Placement: Addition and Subtraction

There is no formal placement test for this program. The minimum requirement for working in the addition and subtraction level of the program is that students have a beginning second grade math computation ability, as indicated by the appropriate placement of students in the second grade level of your math program. Based upon substantial experience with math instruction, we think it is unlikely that you will have many students who have already mastered all or most of the material in this program. Should your find yourself with such students, however, those students should be excused from the program.

Placement: Multiplication and Division

There is no formal placement test for this program. The minimum requirement for working in the multiplication and division level of the program is that students have mastered multiplication and division facts--mastered in the sense of giving correct answers quickly. Based upon substantial experience in math, we think it is unlikely that you will have many students who have already mastered all or most of the material in this program. Should you find yourself with such students, however, those students should be excused from the program.

Components and Pricing

Addition and Subtraction Module:

MS 151 - Teacher's Book: $65.00  Buy Here!
MS 152 - Student Book: $12.00 ea. / $55.00 set of 5 (MS 152K)  Buy Here!

Multiplication and Division Module:

MS 153 - Teacher's Book: $60.00  Buy Here!
MS 154 - Student Book: $11.00 ea. / $50.00 set of 5 (MS 154K)  Buy Here!

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