Mathematics Should Be Taught Using Manipulatives, Visual Representation, And Concrete Materials

strategies and learning tasks to re-engage students (including what you and the students will be doing)

During my first year at a new high school, my pre-ap geometry teacher saw how

The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).

The Case of Randy Harris describes the lesson of a middle school mathematics teacher, and how he uses diagrams, questions, and other methods to guide his students to a better understanding. Throughout his case study, Harris’ methods could be easily compared to that of the Effective Mathematics Teaching Practices. There are eight mathematical teaching practices that support student learning, most of which are performed throughout Randy Harris’ lesson. Harris didn’t perform each teaching practice perfectly, despite doing the majority of them throughout his lessons. The following are examples of how Randy Harris implemented the eight mathematical teaching practices into his lesson, and how the ones that were neglected should have been

Teachers need to be flexible in how students learn and demonstrate their knowledge and understanding. For example, if a student is having trouble keeping up with written work, the student could accomplish a similar learning objective through a different method.

When it comes to mathematics, there are right answers and wrong answers. For many people this makes math an easy process. When one finds them with the wrong answer, it is understood that, somewhere within their problem and process is the error. Common Core is a fairly new process for solving math equations and allows students more techniques to solve everyday problems.

Using hands-on resources and manipulatives in mathematics is important for student’s development of mathematical content knowledge. Knaus & Featherstone (2014. p. 12) state that through the manipulation of objects in a mathematically rich environment children are able to achieve an understanding providing a bridge between everyday concepts and abstract concepts. Furthermore, manipulatives and play are linked. During play with manipulatives such as an age appropriately fill treasure basket children are able to explore a range of objects shapes, sizes, textures, weights, lengths and the mathematical language that is related to the objects (Knaus & Featherstone, 2014). According to, Connell, Shearer, Tobin and Harrod (2006) exploratory manipulatives provide students with the opportunity to explore their

Mrs. Rivera has math and literacy centers in her classroom. Each center consists of several binds and folders with different activities. The math and literacy centers reinforces the curriculum that's being taught within the classroom. There are several different centers under the math and literacy center. For example, Mrs. Rivera has a pattern block center, a puzzle center, a word problem center, a math card center, a game center, an iPad center and an iPhone center for math. For literacy, there is a block center, a pretend center, a big book center, writing center, art center, computer center, movie center, sentence making center, iPad center, read along center, buddy reading center, poetry center and a hand writing center.

Manipulatives and Models to teach Algebra Concepts (6 points) Identify and explain how specific (by name) manipulatives, mathematical and physical models, and/or technology can be used to teach Algebra concepts for the following strands for a total of 3 tools. See Section 2 directions for more detail. Remember to include references and represent at least one concept from the following strand with a minimum of one of each tool (manipulative, model, and technology) represented in the section.

Remember being taught something new in a mathematics class and thinking to yourself, “when am I ever going to use this in life?” Sure, not every mathematical theory taught in class will be used in your career, but from my experience, many of the skills learned in mathematics are frequently utilized each day. While mathematics may not be everyone’s favorite subject, I found it to be not only the subject I use the most outside of school, but the one that I enjoy the most, which is why mathematics is my favorite subject.

Observations for Jose took place on his science and math classrooms respectively. At the beginning of the class, the teacher asked a question to the group, Jose raised his hand to answer. He remained quiet on his desk while teacher explained the lesson in detail to the whole class. During the rest of the class, he remained seated on his desk and participated in the discussion at the proper time. The teacher showed a video to the class and asked some questions, most of the class tried to answer them, but Jose didn’t seem interested as he was with his head down on his arms. Next Day during the math period, students were working in small groups. Jose actively participated in the class discussion. He reviewed his paperwork with his peers and asked a few questions to the teacher’s assistant. Jose followed the teacher commands until the class finished. During the interview process, Jose mentioned that his favorite subjects were reading and science, conversely the subject that gives him most trouble is English because kids in the class laugh at him. Jose thinks that learning is natural for him and he can complete assigned works but doesn’t feel being as smart as the other students. When with his friends, he likes to hang out, play games and soccer. About his other classmates, he stated not getting along with them because they are always pushing or tickling him. Jose reported having no problems with the teachers or at school in general. On weekends, he usually enjoys of playing with

Schweyer further stated that in “using manipulatives in teaching mathematics will help students learn to relate real world situations to mathematics symbolism, work together cooperatively in solving problems,

Observations from Jose took place on his science and math classrooms respectively. At the beginning of the class, the teacher asked a question to the group, Jose quickly raised his hand to answer. He quietly remained at his desk while the teacher explained the lesson in detail to the whole class. During the rest of the period, he calmly remained at his desk and participated in the discussion at the proper time. The teacher showed a video to the class and asked some questions, most of the class tried to answer them, but Jose didn’t seem interested as he was with his head down on his arms. The next day during math period, students were working in small groups. Jose actively participated in the class discussion. He carefully reviewed his paperwork with his peers and asked a few questions to the teacher’s assistant. Jose followed the teacher commands until the class finished. During the interview process, Jose mentioned that his favorite subjects were reading and science, conversely the subject that gives him most trouble is English because kids in the class laugh at him. Jose thinks that learning is natural for him and he can complete assigned work, however, doesn’t feel being as smart as the other students. When with his friends, he likes to hang out, play games and soccer. About his other classmates, he stated not getting along with them because they are always pushing or tickling him. Jose reported having no problems with the teachers or at school in general. On weekends, he

Markworth (2012) suggests ways students can learn algebraic concepts and geometric patterns by developing an understanding of functional thinking. Growing patterns are a useful counting method that allows students to engage with algebra. Geometric growing patterns best support student’s ability to develop functional thinking which is essential. This article outlines three teaching strategies for using geometric growing patterns, these are:

It is important to teach or at least try to teach students problem solving related to math. Problem solving plays a big part in the math process. Teaching problem solving is beneficial to students because helps the students find solutions when struggling. It helps math to be more interesting and less stressful. Students see math with less negative reaction and more hope. Problem solving helps and improves student’s ability to think, solve, and find solutions. It is important for students to have the ability to have problem solving skills and this is what it teaches the students. Ultimately, problem solving helps students focus increase and learn what works best for them.