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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 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 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.