CHAPTER 1
THE PROBLEM AND ITS SETTING
Background of the Study Mathematics is considered as a difficult school subject by majority of the students around the world. In a survey conducted by Gallup in 2005 as cited by Fleming (2014) in her article Why Math is Difficult, 41% of girls and 31% of boys said that mathematics is the most difficult subject. Mathematics can be difficult especially if someone lacks conceptual understanding. Likewise in mathematics education, there are issues where student teachers in math and even some math teachers have difficulty in teaching mathematics because of unpracticed and forgotten concepts, and lack of conceptual understanding in mathematics. According to Kilpatrick, J. et al. (2001), conceptual understanding,
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It is a strategy coined by Jerome Bruner which uses structured inquiry process. Concept attainment strategy is an instructional strategy which focuses on decision-making and categorization processes which leads to the creation and understanding of a concept (Viveka, V. &Rai, E., 2013). In this strategy, the students will discover the characteristics of a group or category that has been provided by the teacher. To do so, students compare and contrast examples that contain the characteristics of the concept with examples that do not contain those characteristics. According to Basapur (2012), this is the best strategy among others because this strategy is designed to help students of all ages reinforce their understanding of concepts and practice hypothesis testing. He added that this strategy will help students to become more efficient at learning. In concept attainment strategy, students distinguish examples and non-examples of a given concept and hence, this will enhance their critical thinking skills and they would be able to explain why such that example is part of the given concept. Through these, students’ conceptual understanding will be enhanced because they are able to explain why those examples worked on the given
theories can be defined as a way that a student grows, progresses, or increases his or her
Antecedents of the Concept The next step in the systematic process of concept analysis is identification of the antecedents (Walker and Avant, 2011). According to Walker and Avant (2011) antecedents are characteristics that must happen prior to the occurrence of the concept. The authors tried to identify antecedents of holism as an approach to the delivery of nursing care.
Conceptual Vs. Procedural Knowledge - Teaching Math Literacy. " Teaching Math Literacy -. N.p., n.d. Web. The Web.
Concept-Based Curriculum and Nursing Programs. Landeen et al. (2016) indicated that to avoid overloaded curriculum, many colleges have moved from the traditional curriculum to CBC. Higgins and Reid (2017) mentioned that concept-based approach operationalizes student-centered learning with purpose and application that promote higher thinking and engagement of faculty and students. According to Erickson, Lanning, and French (2017), knowing the facts is not enough, and they clarified that if the educators want students to develop intellectually, creatively problem-solve, and grapple with complexity, then the key is in conceptual understanding.
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
A. Behaviorism, constructivism and cognitivism are relatively common theories used in the classroom as ways to approach student learning. Behaviorism focuses on observable behavior, such as students answering questions correctly, or being able to follow directions to complete a task as instructed. Characteristics of a classroom that uses behaviorism might be memorization of facts, writing vocabulary words, or a token reward system to inspire the desired behavior and decrease undesired behaviors. Constructivism, as indicated by the root word “construct,” focuses on the construction of new ideas, or expanding on what is already known. Students in a classroom using constructivism as a means for learning might seem more actively engaged in the learning process; they often learn something new through applying what they already know about the content area, and exploring new matter to further their understanding. This type of classroom often uses hands on manipulatives to allow students to actually build, create, or experiment with what they are learning. A cognitivism approach to learning might be explained by the minds capacity to process information – such as how a learner might remember something, retrieve information, or store new concepts. Learning through this method often depends on how the student processes what the teacher is presenting. Classrooms using this approach might incorporate learning strategies that help students categorize and sequence information to assist with processing. Like constructivism, it can be an active style of learning.
Using literacy strategies in the mathematics classroom leads to successful students. “The National Council of Teachers of Mathematics (NCTM, 1989) define mathematical literacy as an “individual's ability to explore, to conjecture, and to reason logically, as well as to use a variety of mathematical methods effectively to solve problems." Exploring, making conjectures, and being able to reason logically, all stem from the early roots of literacy. Authors Matthews and Rainer (2001) discusses how teachers have questioned the system of incorporating literacy with mathematics in the last couple of years. It started from the need to develop a specific framework, which combines both literacy and mathematics together. Research was conducted through
Among many teaching styles and learning theories, there is one that is becoming more popular, the constructivist theory. The constructivist theory focuses on the way a person learns, a constructivist believes that the person will learn better when he/she is actively engaged. The person acts or views objects and events in their environment, in the process, this person then understands and learns from the object or events(P. Johnson, 2004). When we encounter a certain experience in our life, we think back to other things that have occurred in our life and use that to tackle this experience. In a lot of cases, we are creators of our own knowledge. In a classroom, the constructivist theory encourages more hands-on assignments or real-world situations, such as, experiments in science and math real-world problem solving. A constructivist teacher constantly checks up on the student, asking them to reflect what they are learning from this activity. The teacher should be keeping track on how they approached similar situations and help them build on that. The students can actually learning how to learn in a well-planned classroom. Many people look at this learning style as a spiral, the student is constantly learning from each new experience and their ideas become more complex and develop stronger abilities to integrate this information(P. Johnson, 2004). An example of a constructivist classroom would be, the student is in science class and everyone is asking questions, although the teacher knows the answer, instead of just giving it to them, she attempts to get the students to think through their knowledge and try to come up with a logical answer. A problem with this method of learning is that people believe that it is excusing the role of...
As a student in any grade level in school, math is an essential part of education that is utilized quite frequently. It could be connected to managing time or counting dollars and cents. The kinds of people who find math to be fascinating and challeging can be classified as someone who possesses mathematical-logical intelligence.
In a classroom, a teaching strategy is a generalized plan for a lesson which includes structure, instructional objectives and an outline of planned tactics, necessary to implement the strategies. Reece and Walker (2002) describe a teaching strategy as a combination of student activities supported by the use of appropriate resources to provide particular learning resources. It is that procedure by which new knowledge is fixed in the minds of students permanently. For this purpose, a teacher does extra activities in the class. These activities help the teacher to take shift from one strategy to another. A method of teaching on the other hand is directly related to the presentation of the lesson. The choice of the teaching method depe...
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.
greatly to how well they will do at school and also on how this will
Math is probably one of the only subjects that I have really struggled my whole life or more accurately, all my years being in school. Math has been such trouble and really challenging because I cannot really remember mathematical formulas and problem solving methods. It is actually a real struggle when taking a math test or exam, especially a final exam. Trying to remember all those methods and formulas, it makes it hard to think and focus on finishing up all the problems on time. Even though I am often am
Devlin believes that mathematics has four faces 1) Mathematics is a way to improve thinking as problem solving. 2) Mathematics is a way of knowing. 3) Mathematics is a way to improve creative medium. 4) Mathematics is applications. (Mann, 2005). Because mathematics has very important role in our life, teaching math in basic education is as important as any other subjects. Students should study math to help them how to solve problems and meet the practical needs such as collect, count, and process the data. Mathematics, moreover, is required students to be capable of following and understanding the future. It also helps students to be able to think creativity, logically, and critically (Happy & Listyani, 2011,