...Physical Manipulatives Manipulaitves can be classified into two: concrete or physical manipulatives and virtual manipulatives. Domino (2010) categorized these physical manipulatives in three types. First, manipulatives can be objects that are familiar in everyday life, such as beads, buttons, coins, dice, and popsicle sticks. Second, manipulatives can be objects that are commercially manufactured and have multiple possible educational applications but exist primarily for some other purpose such as children’s building blocks, jigsaw puzzles, Legos, and Tinker Toys. Third, manipulatives can be objects that are specifically designed to be used in teaching mathematics, such as attribute blocks, base-ten blocks, color tiles, Cuisenaire rods, geoboards,...
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...Basic Mathematical skills are considered as one of the foundations in mathematics. Understanding the concepts of four fundamental operations – addition, subtraction, multiplication and division of integers will keep the learners confident to step up to higher math but keeps returning to the basic mathematical concepts since K to 12 curriculum is a spiral progression. These operations are also known as arithmetic, the Do-Re-Mi of Mathematics (Byrce, 2016). One of the learners’ gaps who enter in high school has difficulty in their basic mathematical skills and concepts especially in four fundamental operations of integers. Mathematics is commonly identified as one of the most difficult subjects encountered by learners in schools and adults...
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...forms, play that involves mathematics and playing with mathematics itself (2009, p. 327). Further, it is the adult present during the play who is able to recognize how the children are representing their mathematics knowl- edge and then build on their understanding through prompting and questioning. Sarama and Clements stress that “the importance of well-planned, free-choice play, appropriate to the ages of the children, should not be underestimated. Such play … if mathematized contributes to mathematics learning” (2009, p. 329). Educators also provide experiences in playing with mathematics itself by using a repertoire of strategies, including open and parallel tasks that provide differentiation to meet the needs of all students and ensure full participation. Moreover, students do not have to see mathematics as compartmentalized, but instead as it mirrors their life experiences through other subject areas like science and the arts. As such, “high quality instruction in mathematics and high quality free play need not compete for time in the classroom. Engaging in both makes each richer and children benefit in every way” (Sarama & Clements, 2009, p. 331). This equity of opportunity is essential so all students can fully develop their mathematical abilities. A carefully planned mathematics environment enables the use of manipulatives whether commercial products or found objects, sometimes brought in by the students themselves. Ideally, manipulatives serve as learning tools to...
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...for how great our education systems are, but in the last decade, our test scores keep plummeting, particularly in math and science sections. Mathematics is a fundamental course that will affect and influence students for the rest of their lives. That is why it is essential that these students get a firm grasp on the subject at a young age, so that they do not fall behind and into a vicious cycle of always trying to keep up. When it comes to learning mathematics, there are a multitude of different teaching techniques that could be utilized, and in today's educational system teachers need to be adaptive to alternative learning methods, and manipulatives are a great example of that. In this paper,...
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...Michelle is currently enrolled in a functional life skills program in a middle school program. Michelle finds it hard to comprehend number relationships and computation. She usually finds subtraction hard and needs subtraction to be demonstrated by separating sets of concrete objects and explaining the results using pictures and words. She needs verbal prompts, visuals support, and manipulatives to be successful at solving problems. Michelle has difficulty finding numbers greater than 10. A common mistake for her happens when she adds 10 + 11, her usual answer is...
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...restraints and knowing that some of the questions could have more than one answer, I felt the pressure. I used my results from the First Five Years Mathematics Competency Test to identify mathematical areas and concepts that are my strengths and areas that could be developed. I answered all 15 questions correct, but for two questions I didn’t choose all the answers. I second guessed myself which lead to self-doubt of my knowledge and understanding and wondered if they were trick questions. Once reading the questions again, not under time restraints I was able to see the answers and see where I went wrong. The two questions I didn’t completely answer correctly both included counting and explaining. Question two asked for the counting strategies for the equation 2+3. I had chosen the correct answers but also had chosen 3+2 as an answer, this was incorrect. I reflected on this and compared it to Bishop’s Universal activities and identified that this was in the counting category, number, number relationships, number...
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...2. Teach strategies for counting: “Counting seems to be a very simple skill, but can appear very complicated to those who have not mastered it” (Mastropieri & Scruggs, 2014, p. 358). Learning to count will help students in all math skills. 3. Reinforce one-to-one correspondence: With the use of different sets of objects like blocks, counting bears, or candy to match quantities. “Before later concepts can be mastered effectively, it is important that students understand the concept of numerical numeration” (Mastropieri & Scruggs, 2014, p. 358). 4. Use manipulatives for teaching addition and subtraction concepts: “Using such materials as beads, buttons, dried beans, or commercially available base 10 blocks (distributed by companies such as Delta Education), you can help students learn concepts of addition and subtraction by counting” Mastropieri & Scruggs, 2014, p. 358). With the use of manipulatives, students are able to add and subtract by counting objects. 5. Use number lines to promote operations: “A helpful intermediate step between counting actual objects and operating with numbers is the use of a number line” (Mastropieri & Scruggs, 2014, p.359). With the use of a number line students can add and subtract by counting on and counting backwards. 6. Touch Math: The Touch Math system has the students count dots to help them add or subtract two numbers. “Students learn that each number is associated with a certain number of dots (touch points),...
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...Case Study K-5 Math Endorsement ME: Course 1-2013-Bibb Denna R. Bradford 2305 Kingsley Drive Macon, Georgia, 31204 478-719-2943 dbradford.williams@bibb.k12.ga.us Instructor: Mrs. Karen Crider Table of Contents I. Background Information Table on Student 1 and Student 2 ……………... II. Student 1 – IM …………………………………………………………… A. Student Interview. III. Student 2 – AM …………………………………………………………… A. Student Interview IV. Assessment, Discussion, and Presentation of Tasks ……………………… A. Number Sense V. Analysis and Interpretation of Data ……………………………………… A. Analysis B. Interpretation of Data VI. Misconceptions ……………………………………………………………... A. Student 1 – IM B. Student 2 – AM VII. Intervention Plan …………………………………………………………... A. Student 1 – IM B. Student 2 – AM C. Anchoring Instruction Activities………………………………………. VIII. References …………………………………………………………………... 2 3 4 5 6 7 9 10 11 I. Background Information Table on Student 1 and Student 2 |Background Information ...
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...Case 3 In this case study, we look at four Year 4 students, Jake, Remy, Molly and Eliza, who have been given the task of problem-solving. They are making a square-based pyramid with 140 oranges. Each student has taken on a different job. They will be using materials to construct the pyramid to get the answer to their questions. Theories from both Piaget and Vygotsky will play part in their thinking. As well as help from the teacher. Using manipulatives allow the students to create their own cognitive models. Not only do the use of mathematical manipulatives have the advantage of engaging students, it also heightens the interest and enjoyment of mathematics. (hand2mind, 2017). The National Council of Teachers of Mathematics (NCTM) (as cited in hand2mind, 2017) advocate the use of manipulates within the classroom, they believe this...
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...that maximize student learning. Students can use recognition of their individual learning styles to find what study methods, environment, and activities help them learn best. (Cathryn Whitehead, eHow Contributor) According to Cynthia Hockman-Chupp (2011) on her article "Let Me Learn My Own Way", students have their different approach in Mathematics depending on their Jungian learning style. Specifically mentioned are student preferences for gaining energy (extraversion or introversion) and preferences for processing information (sensing or intuition). Consider your own learning style and that of various students as you look at "Four Ways of Learning" as quoted; "Let me master it!" (Preferences: introversion and sensing). They like direct instruction and practice work, and they dislike experimenting unless they can receive immediate feedback. "Let me do something!" (Preferences: extraversion and sensing). These students learn through movement, interaction, and hands-on manipulative. They often use a purposeful trial-and-error method working with pictures or manipulative to solve problems until they "see" that their answer matches the mathematics of a problem. "Let me think!" (Preferences: introversion and intuition). These students process ideas internally and they are into concepts, not procedures. "Let me brainstorm!" (Preferences: extraversion and intuition). These students process their ideas best out loud with partners or in groups. Algebra success depends on certain factors...
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...Pre-service coursework is a highly researched need of reform in the educational field as it relates to teacher preparation. Researchers vary in their viewpoints on what constitutes an effective course for practicing teachers, but the objective is clear with better programing for beginning teachers, the more effective these teachers will feel in the field and will be more likely to stay in the profession. One viewpoint on how to reform a course to make it more effective comes from an Australian study details researchers restructuring a course on teaching mathematics to include opportunities for teachers to practice teaching mini-lessons. Along with teaching these lessons, there would be collaboration and feedback from classmates. The researcher’s...
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...Geometry Manipulative Handout Joan L. Holyfield Math/157 March 8, 2015 Instructor: James Paga Geometry Manipulative Handout The geometry manipulative that I chose to present is how to make a Geo City. With making a Geo City, it teaches students in grades 3-5. This math exercise encompasses learning and identifying cubes, pyramids, cones, rectangular and other shapes in different sizes which are appropriate for this age group. This activity can be done in a group setting, with each child having a share in identifying different geometrical shapes, and putting them in a real-world setting. By using these different geometric shapes to construct buildings and cars, the children will learn about spatial visualization, location and coordinate points, and transformation. The Geo City will help to reinforce the relationships with two and three-dimensional shapes that have already been learned in previous classes. The students will also be able to explore the effects of rotating, reflecting, and transforming shapes. The Geo city also lends itself to real world application by simulating a city block that they may find in their neighborhood. Then they can begin to understand how the geometric shapes are a part of their everyday lives. Constructing the Geo City also helps the children with their mapping and graph skills, because they will be using both to first, decide how to design the city (using graph paper or geo dot paper), then by deciding where to put the houses...
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...The Importance of Number Sense in the Elementary Classroom Robyn Thomas EDU Instructor: Dr. Silvernail November 2, 2011 Abstract In today’s elementary classrooms, students are expected to think and speak on high levels of intelligence. Teachers are encouraged to set high expectations, to question and probe and to ask students to explain what they are thinking. This paper will focus on the importance of understanding numbers or possessing number sense at the elementary level. The idea that students should already have some number sense is controversial. Struggling students in today’s classroom in the area of math seem to lack a major concept, which is a basic math skill or understanding numbers. What is number sense? Number sense refers to a person's general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems. Number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. Most children acquire this conceptual structure informally through interactions with parents and siblings before they enter kindergarten (Marshall 2010) . Other children who have not acquired it require formal instruction to do so. For example, one child may enter school knowing that...
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...communication, as a guide to belief and action. This kind of thinking can be learned easy in mathematics since the length of students stay in the school are maximized with lots of enjoyable activities, active participation, and worthy learning experiences thus, the skills needed by the students will be given deeper emphasis by the teacher and the school personnel. The use of appropriate tools like calculators, manipulative objects, measuring devices, computers, smart phones, tablet PCs and the internet is very essential for students’ development of critical thinking skills wherein they can explore and answer their personal problems or confusions by using appropriate tools allowed for them. If these tools can only be used correctly and effectively by students, we can produce students that are globally competitive and can bring pride to the Philippines with no doubt. The principles followed by the K-12 Basic Education Curriculum will ideally bring great change to the educational system of the Philippines. Students nowadays are very exploring especially in computer generated knowledge and experiences and make some self-study which I can say very effective in gaining vast amount of in-depth knowledge on their own. Therefore, I can strongly say that these principles are suited for them and if eternalized by the students and teachers can give a big change to our fact-finding students. The mathematics curriculum allows for students to learn by asking relevant questions and discovering new...
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...Teaching Mathematics Teaching Mathematics My interest in teaching mathematics came from the experience of helping others. I have always enjoyed learning math, and I realized that I also like helping other people learn math, especially those that struggle with it or those who have a disliking for it. As a teacher, I will be able to fulfill my aspirations; both my students and I will learn together and from one another. I feel that it is important for me, as a teacher, to stay current and deepen my understanding of mathematics and mathematics education. My learning will continue from my experiences and interactions as a teacher, helping me to become a better educator. I must always be willing to learn from the things I do and use this to better my teaching style, which will, in turn, benefit my students’ learning. To begin, I want to be able to benefit my students’ learning by aiding them in understanding math and realizing that, although they may not think so, math is practical in real life. In particular, I want to work with students at the secondary grade level because as kids get older they seem to lose their enthusiasm for learning, especially in mathematics. I would like to help my students maintain an interest in all their learning, especially math. Also, it is important when teaching to satisfy the needs of all students in the classroom. Everyone should have the opportunity to learn. However, this can sometimes be a difficult task because learning happens in a variety...
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