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This article focuses on Math Promise, a contract containing the commitment of children and parents to spend mathematical time together and get to know each other's mathematical thinking and understanding. Topics covered include how the Math Promise began in one classroom, examples of opportunities parents can take advantage of to do math with their children, and the benefits offered by Math Promise. Mentioned also are resources which can help teachers and parents launch the Math Promise.

A personal narrative is presented which explores the authors' experience of teaching mathematics in the rural community of Santa Avelina in Guatemala.

The article presents creative solutions to answer a middle school mathematical problem. Various representations were used by students to model the problem, including pictures, symbols, and numerical reasoning. Examples are provided of works from students that exemplify the differences in the methods used to solve the problem. Accounts from several mathematics teachers about the mathematics problem are included.

The article offers suggestions and ideas for elementary school teachers on how to build connections between children's mathematical thinking and family and community knowledge in mathematics instruction. Topics mentioned include the importance for teachers to know their students as well as their families and communities, tips for engaging with the community through visiting locations identified by students, and guidelines for designing standards-based mathematics lessons.

The author discusses a middle school learning activity entitled "Influential Figures in Mathematics: An Overview With Web 2.0," which involves the use of the online timeline software Timeglider for promoting equitable mathematics. Aside from enhancing use of technological tools, he explains that the assignment also allows students to gain cultural understanding of mathematics. He also offers insights on Timeglider features and outcome of the classroom presentations delivered by his students.

The article offers information on the number puzzle called Oki-Doku. According to the author, Oki-Doku puzzles could improve children's mathematical fluency because it is easy to understand, it involves developing number-and-operation sense, and students working on it will not need outside agent to tell them if they are correct or not. The author states that these puzzles are easy to make and can be tailored based on the student's need.

The article discusses the Great Mathematician Project (GMP), an initiative designed to accommodate the special learning needs of gifted and talented students about mathematics. The project's purpose directly addresses the National Council of Teachers of Mathematics (NCTM) Equity Principle (NCTM 2000), and is based on the Autonomous Learner (AL) model developed by George Betts. It also describes the seven stages of the GMP.

The article focuses on how teachers could communicate mathematical ideas in the classroom. It is noted that during the early stages of dynamic view including learning, graphing, substitution, using the metaphor of continuous motion and working only with continuous functions is helpful. It is asserted that it is not sufficient to communicate mathematical ideas to students although knowledge of mathematical content is necessary.

The article presents a project which students are asked to design two versions of the packaging for a product of their choice and look at the various mathematical calculations by simulating a real-world marketing situation. It states that students must calculate the volume of the packages and are required to consider surface area as they analyze the cost. Also included is a table that reflects the scoring rubric for students who did the project.

The article provides mathematical concepts to help students develop their learning capacity for transfer. It highlights the different concepts in learning transfer including transfer via connections, transfer via contrasting ideas, and transfer via error analysis. It offers guidelines for aiding the students ability to transfer including the importance of building on student's experiences, and the use of instructions that deepens the student's mathematical knowledge.

The article discusses problems solving as a way of teaching mathematics. It says that problem solving placed emphasis on the learning skills of students. It mentions that the problem-solving abilities of a student could be improved through the experiences they gained in understanding the mathematical situations. It states that presenting question in real-life, which encourage the students in finding mathematical solution, leads to broader conceptual understanding.

The article focuses on the review-first approach for the retention of mathematical knowledge in students upon entering a new academic year. It notes that the approach leads to the delay of introduction of new lessons with students spending their time for reviewing materials from the previous grade. It also features the Comprehensively Applied Manipulative Mathematics Program (CAMMP) approach to teaching which will help reduce the need for review and accelerate the learning ability of students.

The article offers the author's insights on his use of the book "12 Ways to Get to 11," in teaching mathematics to his fourth-grade students. He states that the book provides an amazing presentation by mathematically demonstrating, through pictures and words, twelve likely combinations of details that total to eleven when they are added. He mentions that he introduced the game played in the television program entitled "Jeopardy," wherein the solution to the question is already provided to the contestants as the contestants, in turn, must give the right question in order to attain the answer. The author concludes that the book offers an amazing segue into thinking on number combinations, as he is pleased with his success in teaching mathematics using the book.

The article focuses on the essential development of mathematical mind habits among middle grades regarding the mathematical transition from arithmetic to algebra. It features the use of habits-of-mind approach in high school curricula organization. It states that the approach offers comprehensible knowledge on mathematics and provides a vehicle used for decreasing mathematical techniques and methods used in high school which will only leaves a set of general purpose tools for the subject. It also mentions that the key for mathematical learning of students in the U.S. is building coherence in mathematical ideas development.

This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (N= 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially developed curriculum, the University of Chicago School Mathematics Project curriculum, or National Science Foundation-funded curriculum comprised the sample. Of interest were comparisons of the difficulty level and grade in their initial and subsequent college mathematics courses, and the number of mathematics courses completed over 8 semesters of college work. In general, high school curriculum was not differentially related to the pattern of mathematics grades that students earned over time or to the difficulty levels of the students' mathematics course-taking patterns. There also was no relationship between high school curricula and the number of college mathematics courses completed. [ABSTRACT FROM AUTHOR]

The article discusses topic related to the mathematical problem chords of circle to triangular numbers to volumes of spheres. It denotes that this kind of delving deeper is different from its other kind since arose from a telephone conversation inspired by mathematician Don Crossfield. It also presents the conversation between Hypatia and Ptolemy concerning the problem raised by Crossfield which was published in "The Oregon Mathematics Teacher." According to the article, the conversation is composing of a casual talk and confusing reference that occurred in a casual conversations.

The article discusses topic related to the importance of learning various methods in solving mathematical problem. According to the article, students such as those that can easily find a way to solve problem will become better problem solver and have a deeper understanding of mathematical concept is they can recognize and adapt various problem solution strategies. The article also discusses the Principles and Standards for School Mathematics (NCTM), define proficiency in mathematics as the ability to use knowledge flexibility.

The article discusses topics related to the proof and prealgebra curriculum. It highlights that prealgebra curriculum offers opportunities for motivating students engage in proof and for cultivating proof readiness. It explains that prealgebra curriculum presents numerous opportunities that encourage the students to justify their interference. It accordingly requires the students to clearly communicate and to reason out their solutions to mathematical problems with appropriate mathematical languages and notations.

The article discusses topic related to the importance of diagrams and representations in understanding mathematical solutions. It highlights that mathematical representations helps the students organized thinking, since they bring a visual components to abstract ideas and serves as template for computation with comprehension. On the other hand, the inevitability of representations is not accordingly a guarantee that they can be used effectively. According to the article, the focus of the mathematical representation and their connection began during the publication of "Curriculum and Evaluation Standards for Mathematics" (NCTM).

The article discusses topic related to the relationship between the slopes of perpendicular lines. It denotes the use of the Geometer's Sketchpad (GSP) to allow student discover a property of slopes. It examines the range of values the slopes might have and provides an example of result the student might generate. It also presents the laboratory sheet with instruction and notes for teachers to help students who encounter problems. According to the article, with the use of GSP, the students might be able to discover that slopes of perpendicular lines are negative reciprocal to each other.

The article presents the answers and solutions for several mathematical problems published in the previous issues of the journal. It includes the solution of the problem number one which shows degree of vertices at the circle labeled A-H. Solution of the number two problem concerning the radii of circles related to the problem number one. The solution of problem number three is also mentions related to the vertex angle of the isosceles triangle at the center of the square.

The article discusses topic related to the particulars of proofblocks. It explains that among the difficult topics in geometry includes the concept of proof. It discusses the intuitive approach of teaching proof, which is the proofblock, that makes proof accessible to students without sacrificing the rigor of traditional approaches. It denotes that with the use of ProofBlock, the student will be able to find it natural from both ends of their attempted proof. It also mentions that ProofBlock is an inherently visual approach which uses manipulative that addresses the need of visual and kinesthetic learners.

The article discusses the concept of basic trigonometry and evaluates its applicability to the sixth-grade class. It offers an overview of the history of mathematical ideas under the trigonometry and their development in the field of academics. It also explores on various topics in the subjects which include the right triangles, pythagorean theorem and basic trigonometric ratios.

The article discusses the practical method for teaching the fundamental algebraic concept of slope which will relate the rate of change in students' experiences outside the school. It offers an overview of the activity which provides the students with mathematical tasks for their better understanding of the topic and presents the evaluation on their participation. It also explores the hands-on activity which applies the Hooke's Law.

The article provides techniques to define the relationship between greatest common factors and least common multiples through prime factorizations. It explores the concepts and properties of divisibility, prime and composite numbers, as well as exponents. It also discusses the procedural teaching conducted to students in which a visual model for prime factorization is created with the use of building blocks.

The article discusses the concept of the application of physical models or manipulatives in the mathematical discussions. It offers an overview of the basic components of Jerome Bruner's theory which include enactive, iconic and symbolic and discusses their impact on teaching instruments for algorithms. It also explores the active participation of students in an activity which uses manipulatives for various mathematical tasks.

The article introduces a method for middle school students to understand the multiplication of binomials and produce the equivalence (a+b)2 = a2 + 2ab + b2. It presents various problem representations which help students to create algebraic notation for multiplying binomials by naming and seeing quantities in various ways. It also offers an overview of problems wherein the two-dimensional array representation and an area model for squaring binomial is used.

The article discusses the practical application of an origami activity into a problem-solving session. It suggests that the activity utilizes various mathematical concepts such as linear measurement, area, volume calculations of rectangular solids and relative reasoning. It offers an overview of the group activity in which the students calculate the volume of origami with regards to the corresponding sizes of papers. The step-by-step instructions for creating the origami are also illustrated.

The article discusses the use of mathematics in modeling and designing picket fences. It highlights the need for students to recognize the need of using mathematics in particular, concrete context and choose the function the represents the situation mathematically. It explores the use of picket fences as mathematical models. It cites the identification of mathematical forms in contemporary styles and types of fences. It also indicates the reversion of the process in identifying mathematical models for picket fences.

The article presents a response by Kaminski and colleagues addressing a commentary by Jones regarding their research on the effects on figurative transfer of learning mathematics. Kaminski and colleagues disagree with Jones' comment regarding the similarity of the generic representations used in their research to the transfer domain than the concrete representations. They argue that their research have data supporting the success of domain transfer when the concrete representations presented in quantities. They cite that sound theory and theory-grounded empirical findings may encourage the understanding of learning and transfer. Additionally, Kaminski and colleagues expressed their gratitude to Jones on raising the concerns on the query regarding which components affect transfer.

The author reflects on the generalization given by Kaminski and colleagues in their pattern game study that sets to establish the effectivity of generic instantations in presenting mathematical concepts over concrete examples. He notes that the transfer task is biased since it is more similar to the rules involved in the generic instantation condition. He states that more studies similar to domain problems of Koedinger and colleagues must be made before making sweeping generalizations.

The article focuses on the importance and promotion of mathematical conversation in the classrooms. It discusses that such conversations can be used to make students question, talk, agree or disagree over mathematical problems and to let them explore mathematical concepts. It reports on the ways the teachers can establish a community in the classroom and promote discussion amongst them. It mentions the difference between cognitive discourse and the motivational discourse in classrooms. It also mentions the ways to judge the quality of the discourse along with different levels of discourses in a Mathematics classroom.

The article focuses to explain that student's attempt to interpret mathematical problems fosters their mathematical investigations. It employs the technique of implementing discussion based mathematical investigation in a classroom. It uses the Principles and Standards for School Mathematics, which encourages students to discuss their mathematical problems with their classmates. It presents a detailed description of the investigations, which includes assigning problems to students, discussing their solutions in large groups, nourishing their problem solving skills. It describes the progression of problem solving in students, while solving the cereal box problem, that involved arranging 45 cereal boxes. It also stresses on the teacher's role in developing students' mathematical skills.

The article discusses a mathematical problem, that asked to arrange the digits 5, 6, 7, 8, and 9 in a two-digit and a three-digit number, so that their product produces maximum result. It explains methods employed to achieve the solution. It describes an informal approach, which is based on common sense and presents four cases using this approach. Another approach explained is the formal approach, which compare all the four cases in pairs. It also addresses other problems that arise, while solving the original problem. It arranges the problem in 3 cases to analyze various probabilities that result from the problem.

The article presents information on teacher-orchestrated classroom argument discourse, a reform of classroom discourse. It mentions that the discourse aims to use the ideas of students as a source of mathematical ideas in the classroom community. It mentions the role of teacher in initiating mathematical argumentation, which helps the students in constructing their own mathematical explanations by reflecting on the ideas of other students. A classroom example of the teacher-orchestrated classroom argument discourse is presented. It mentions several benefits of the discourse, involving the students in mathematical argumentation and developing their identity in a mathematical community. Also mentioned are the complexities that are faced by the teachers, while conducting the discussion.

The article focuses on a writing workshop organized in a Mathematics class, to enhance community practice of mathematical discussion. It mentions that the workshop is a modeled group collaboration that engrosses its participants in controlled but thoughtful discourse of written assignments. It discusses the processes followed during the workshop involving a participant reading aloud an assignment while others are writing in its response. It mentions a specimen of writing responses which includes writing an introduction, mathematical discourse and conclusion. It discusses that such workshops help participants in better understanding of mathematical problems, enhance mathematical vocabulary and provide them an improved learning experience. Also mentioned are various categories of responses.

The article presents methods of coordinating discourse in a classroom by using an inductive model of teaching. It discusses univocal discourse that involves dialogues and feedbacks from a teacher only, and the dialogic discourse involving exchange of ideas between teacher and students. It reports that the National Council of Teachers of Mathematics has realized that the type of discourse and its quality promotes mathematical understanding. It mentions a program that involved a mix of univocal and dialogic discourse in combination with an inductive model of teaching. It discusses that the model was developed after analyzing an eighth-grade algebra class. It also reports that the model promoted better mathematical understanding amongst students.

The article offers the author's insights on creating a perception of mathematics in the U.S. as being an accumulation of facts rather than a subject involving a creative use of the mind. He discusses an approach called teaching to intuition wherein teachers formulate activities that contribute to understanding and utilize such understanding to explain the rules. He presents a word problem which could be taught to allow students to use mental activity instead of relying on a memorized process.

The article discusses Lissajous figures in mathematics. It explains that Lissajous figures are not usually included in most secondary school mathematics curricula, however, they can provide a fertile ground for students to explore real-world mathematics. The article presents a historical background of Lissajous figures, which were created by Jules Antoine Lissajous, a nineteenth century French physicist for whom the figures are named. The article also discusses the generation of Lissajous figures in a calculator.

The article presents a mathematical problem regarding the number of cows in the pen. It offers an overview of various computations of students and illustrates how they arrived with the correct answer. It also evaluates the answers of the students and suggests that the tasks helped the students to work on generalizations.

An essay which explains the author's position on his argument regarding the features of the cases used on the research of Kaminski and colleagues which have impact on performance is presented. He further analyzed the differences between generic representation and concrete representations to reinforce his claim on the similarity of the transfer task to the two representations. He believes that the results of the research of Kaminski and colleagues were not about mathematical domains phenomenon.

An introduction is presented in which the editor discusses various reports within the issue including "Family Game Nights," by Stephanie Kessinger, "The Math Promise: Celebrating at Home and School," by Danielle Legnard and Susan Austin and "Mapping Our World," by Jim Barta and Joan Kyriopoulos.

The article offers recommendations for the implementation of a math training program by a school math coach. Suggestions include using district content maps for planning meetings among students, drafting a calendar of 30-minute study session dates and providing information on instructional strategies in curricular explorations. It also advises on complementing the teachers' math instruction.

The article shares a publication reader's favorite mathematical lesson, focusing on German mathematician Karl Frederick Gauss and his method of mathematical summation. A brief historical information on Gauss contribution to mathematical lessons and concept is mentioned. The author also provides a sample mathematical problem and solutions to Gauss' summation.

The article presents several comments which show appreciations in the cartoon corner "Taking a Pulse "Back in the Day," by Jim Unger in the October 2009 issue which presents word problems on heart rates. One of the readers said that the students enjoyed the activity in finding their pulse rate. Another one claims that the cartoon was a good activity to use for the learning of the students.

The article reports on the publication and its sister publications' need for manuscripts that promote discussion and dialogue about important issues related to mathematics curriculum. The three journals "Teaching Children Mathematics," "Mathematics Teaching in Middle School," and "Mathematics Teacher" announces that it will provide a forum in their publication open for discussion across a K-12 audience. The article offers possible topics for a curriculum-focused K-12 series. The article also includes contact details for questions or comments.