Solving The Mathematical Tasks As A Framework For Reflection

This paper will demonstrate the pre-service teachers’ understanding of mathematical practices as part of the Common Core State Standards in Mathematics. It will address two specific standards for Mathematical Practices, describing the essence of both and providing a description of how teachers facilitate these practices and how students are engaged in the practices.

The aim of this reflective essay is to evaluate my professional development whilst undertaking the role of the Developing Intra-Operative Practitioner/ Advanced Scrub Practitioner (ASP). Using a reflective model I want to see how my new role affects me as an Operating Department Practitioner (ODP) and any legal implications it has for me as an employee.

As a student, I always enjoyed math. In high school I took all of the offered math classes, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I did not already know? Contrary to my expectation, the first day of class, I learned things about math that had never been brought to my attention. This paper will discuss what I have learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.

Another idea to improve mathematics performance in elementary level is to encourage the student to link the existing knowledge and the new knowledge effectively while working math problems/examples. A worked example is “a step-by-step demonstration of how to perform a problem” (Clark, Nguyen, & Sweller, 2006, p. 190). This will prepare the students for similar problems in the future as they bridge the connection between the problems and the examples. In many cases, students are encouraged to link the informal ideas with the formal mathematics ideas that are presented by the teacher to be able to solve problems. When students examine their own ideas, they are encouraged to build functional understanding through interaction in the classroom. When students share among themselves on differences and similarities in arithmetic procedures, they construct the relationship between themselves hence making it the foundation for achieving better grades in mathematics. Teachers can also encourage students to learn concepts and skills by solving problems (Mitchell et al 2000). Students do perform successfully after they acquire good conceptual understanding because they develop skills and procedures, which are necessary for their better performance. However, slow learning students should engage in more practice

Marilyn Burns attest to the fact that more learners are unsuccessful in math than any other core subject, Dylan William’s believes with application of principles effective lessons can be constructed to take shape where learners can progress to the top 5 in intercontinental standings in math. Robert Marzano, on the othehand, ascribe to vivid learning objectives with employing the chunking procedure to increase learning along with continuous check points for

making Practice-Based Learning work Reflection on PRACTICE A resource commissioned by the Making Practice Based Learning Work project, an educational development project funded through FDTL Phase 4 Project Number 174/02 and produced by staff from the University of Ulster. www.practicebasedlearning.org Author Patricia McClure School of Health Sciences, University of Ulster www.practicebasedlearning.org contents Reflection on Practice 02

Digging through the recycling bin of the math supervisor's office, I pull out an old piece of paper with typed font on one side, and blankness on the other -- perfect. “Mom,” I say, looking up with my four-year old eyes, “Do you have a pencil?” She goes into her purse to retrieve one, eager to see what simple drawing I could create as we waited for my dad (who was a math teacher at the time) to come out of his meeting. However, as she is searching, I waddle right up to the bookshelf and pursue my options. A vast array of different grade-level textbooks were laid out before me; the third-grade option seemed most suitable. I took my pencil, the book, and the paper, and sat sat down at the table to see what I could make of the advanced problems.

“Each event is as completely unexpected as a ghost at the top of the stairs. Or the existence, in a ordinary classroom, of a profoundly beautiful object called pure mathematics” (King 15). In Jerry P. Kings novel, The Art of Mathematics, he presents the idea that most people go through math classes from elementary to high school not because we enjoy it, but because it is a requirement. We are taught simple arithmetic to trigonometry, bisectors within a triangle, and how tall a tree is by its angle from the top to the ground. While many do not find the importance or application between math and our daily lives, it is generally found boring and useless. It doesn’t help when some math teachers are just as uninterested, or find just a little value of math as the students. King continues on to explain how this

During the observation time I was placed in a first grade classroom. Walking into the class I began to look around and smile, there was so much color all over the classroom I could not help but feel happier. The teacher immediately stopped the class and told us what they were doing that morning and had each student introduce themselves to us. They went around and stated their name and then went back to their math workbook. When they were finished with their math worksheets they were then able to pick something to do around the room. That included reading on their own, getting to use the iPad, working on the computer, etc. Some students were together while others chose to work on things independently.

When thinking about cognitive load, it may be useful to think about the total amount of mental effort used in working memory. The cognitive load placed on working memory is considered to be a critical factor in determining learning and problem-solving efficiency, and instructional design requires an alignment with the individual learner’s cognitive capacity and expertise (Sweller, 2012; Sweller, Ayres, & Kalyuga, 2011). Working memory is generally considered to have limited capacity (Schmeck, Opfermann, van Gog, Paas, & Leutner, 2015; Sweller, van Merrienboer, & Paas, 1998). Cognitive load theory recommends instruction organized in such a way to ensure limited working memory resources focus on intrinsic as opposed to extrinsic cognitive load (Choi et al., 2014). Cognitive load theory (Sweller, van Merrienboer, & Paas, 1998; 2011) incorporates a lens through which such an investigation can occur. The theory argues that the cognitive load placed on working memory is a critical factor in determining learning

In today’s society mathematics is a vital part of day-to-day life. No matter what a person is doing at home or at the workplace, he/she is constantly using different mathematics skills to simply function. Then what does this mean for mathematics education? When someone needs to utilize a skill every day then he/she needs a strong background in the skill. Therefore, today’s students need more than a just a working knowledge of mathematics or enough knowledge to pass a test. Today’s students need to understand how mathematics works and how to utilize mathematics skills in the best way possible.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics has always been a difficult subject for students. Many children have developed phobias and barriers towards mathematics, which prevail into adulthood, thus limiting their potential. This limitation implies problems of learning, resulting in the child a sense of inferiority.

Through the use of a small mathematical modeling group the relationship between metacognition and mathematical problem solving was looked at to understand it more in regards to situations and contexts without prompting by teacher. This article questions how the selections of metacognitive strategies come about. The goal of the study being to characterize contexts and situations that give rise to metacognitive activity.

Instruction in problem-solving skills begins at an early age for students. The strategies and techniques used in developing these skills are introduced in elementary schools, typically in a mathematics lesson. The four steps for problem solving in mathematics as identified by Pólya (2004) are: understanding the problem, devising a plan, carrying out the plan, and reflecting on the problem. For the first step, understanding the problem, this is where the student attempts to decipher what the problem is asking, and what information has been provided in the question. Devising a plan is where the student develops strategies to solve the problem. This is where a picture or diagram can be created and /or mathematical relationships can be used to describe the problem. For carrying out the plan, the student will look to their diagram or mathematical relationship and take what information they have discovered form the original problem to see if they can solve the problem. The last step is looking back to the original question to determine if the solution they have found answers the original problem. This is a familiar strategy used by most teachers in school to impart to their students how to solve a word problem.