Module 11: 8 Math Practice Standards

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.

In 2010 majority of the states in the U.S. adopted the Common Core State Standards (CCSS). These new standards were built on the best of high-quality math standards from states across the country. They also draw on the most important international models for mathematical practice, as well as research and input from numerous sources, including state departments of education, scholars, assessment developers, professional organizations, educators, parents and students, and members of the public. The CCSS provide clarity and specificity rather than broad general statements. The CCSS stress conceptual understanding of key ideas, but also by continually returning to organizing principles such as place value and the laws of arithmetic to structure

This paper serves to compare the National Council of Teachers of Mathematics Standards for Secondary Mathematics (NCTM), Common Core State Standards (CCSS), and Virginia’s Standards of Learning (VSOL). The comparison will include similarities and differences among the three documents as well as discuss their strengths and weaknesses. Lastly, a combined set of standards will be developed and presented, encompassing the strengths of the various standards.

Parents are concerned with the changes being made in the way their children are taught math. They are outraged that Common Core wants to cut memorization tecniques like “PEMDAS” and cross-multiplication that “help kids get the right answers to difficult [math] problems.” In contrast, experts believe that techniques “allow students to skip…conceptual thinking.” Also, Common Core math standards claim that getting the correct answer is only the first step, students must then “understand the

There’s no denying that education is constantly changing, but what’s truly astounding is the difference that can be throughout the years in math. More is changing in math classrooms than the tools that are used. The expectations that 21st century students face are completely transforming the approach that’s being taken in classrooms across America. The United States wants to make sure its students are ready to compete on a global level, and teachers are stepping up to the plate. The National Council of Teachers of Mathematics (NCTM) has led the movement for education reform in mathematics.

In the Information Capsule from Miami-Dade county different researchers have developed strategies that a teacher can use to reduce the effects of math anxiety in a student who may be suffering from the phobia. The result of the research has found that a teacher, practice has a strong influence on students’ math anxiety. One way a teacher can reduce math anxiety is to be knowledgeable in their content when comes to math and to always exude a positive attitude towards math. The teacher needs to have more training on the subject of math so they will not lack confidence when they are teaching their students. The recommendation is for teachers to attend workshops on research-based best practices

Students are able to learn to work with logic puzzles and other problems to establish understanding. “Mathematics’ concepts such as money, measurement, size, shape, addition, subtraction (which leads to being able to do bookkeeping, balancing checkbooks and bank statements, buying goods and services)

Right-angled trigonometry 153 Bearings 158 Trigonometry with obtuse angles The sine rule 166 Area of a triangle 172 The cosine rule 175 Miscellaneous problems 180 Surveying 185 Chapter summary 191 Multiple-choice questions 192 Short-answer questions 193 Multi-stage events 195

One of the areas that students find most challenging is math. For the past three years I have been teaching The Flexible Learning program, which covers 6th, 7th and 8th grade Mathematics. The curriculum is was created by both the district curriculum staff as well as the federal programs department of the school system. The Flexible Learning Program (FLP) focuses on mathematics for grades 6-8 for students who are at the highest risk academically. The program is supplemental to the student’s CCGPS classroom, remedial class and Title I support. The curriculum in the classroom is aligned to the Common Core Georgia Performance Standards adopted by the state.

When in math class many students say, “What is the point of math I am never going to use it.” That statement is not true, math is used on a daily basis in our everyday life. “Mathematics is the queen of science, and arithmetic the queen of mathematics” (Carl Friedrich Gauss). Not only is math a tremendous part of everyday life but it is also a substantial part of education. Education is something that many people are passionate about, but many people overlook how much influence math has on other subjects. Understanding the importance of math in education will help students` succeed. Mathematics can teach students’ information valuable to their future. Math is valuable to succeeding academically, learning skills, and the development of young children’s minds.

“Mathematics” is a polarizing word for many people and very often it evokes numerous personal reactions, commonly an anxiety reaction. Surprisingly, I am not speaking here only about students, but more importantly about the people who teach mathematics. As the study done by Alan B. Bates, Nancy I. Latham, and Jin-ah Kim indicated, many teachers have fears about teaching mathematics and how teachers’ fears influence students, their learning outcomes, and how mathematics has impacted them in their years of teaching. These finding are also relevant to how I felt about teaching math due to lack confidence in my teaching abilities of mathematical content knowledge. However, as I am reflecting on this past semester that I spent learning about math trajectories as well as math content knowledge, I feel much more confident in exposing my students to math. I think that mathematics is not an easy concept to teach and it requires good strategies to be a successful teacher, but if we do not try to teach it, we will never gain confidence in it.

According to Anthony and Walshaw (2009), mathematics teachers are effective when they plan learning experiences that build on students’ existing skills and experiences. In order to build in this way, teachers must be knowledgeable of these skills and experiences. From this standpoint, it is imperative that teachers become aware of the students’ proficiencies and experiences in mathematics. Possible means for obtaining this information could be from the students’ former teachers, previously taken standardized tests, and prior academic records (e.g. report cards and transcripts). Recognizing that these items may not be all inclusive, especially if the students have experienced mathematics outside of a formal school setting, teachers should also gather information directly from the students. The teachers could administer assessments to gain some indication of the students’ mathematical proficiencies and could interview the students in regards to their mathematics experiences.

During my Junior HS and Senior HS math experiences, I needed relatable real-life connections and the problem happening in the real-life situation so that I was clear how and why a certain algorithm would solve the problem. I struggled continuously with the strategy of the solution before all students understood the problem in the real-life situation has been the order in every math class I have ever taken. Another issue was, the process to work through the algorithm. Proceeding through steps to solve the problem, would give meaning if demonstration of the process included describing why you are doing what you are doing (ie. multiplying, subtracting, dividing, or adding). As a student, the details in greater specificity was very important to my comprehension. I needed to know how the mathematical algorithms and solutions evolved. I always felt like I needed the question “what happened that caused the math problem to need a solution answered.

Current and past research, practices and theories have all shaped and guided curriculum and pedagogies in maths classes in the 21st century (Bayetto, 2016). Lambdin & Walcott (2007) examined six phases over the last hundred years, including drill and practice, meaningful arithmetic, problem solving and the more recent, standards and accountability. With reference to teaching numeracy, some theories support this capability more than others. According to Lambdin & Walcott (2007), the drill and practice era supported connectionism and teaching skills and facts through teacher demonstration and repetitive practice. Whereas the meaningful arithmetic phase emphasised acquisition of mathematics to support workplace skills, with activity-based lessons and encouraged learning through experiences and activity-based lessons, rather than systematic, explicit teaching. When planning a maths program, teachers must consider and reflect on the current pedagogy, guided by their own professional beliefs and the theories and evidence-based practices that shape these beliefs (Bayetto, 2016).

Learning math skills is critical for establishing a foundation for success in mathematics. The model intends to promote and develop students’ mathematical skills and knowledge. Also, the model is designed to build a strong mathematical foundation for students. As students have individual differences, the model employs several learning theories to meet students’ learning needs and achieve their potential in mathematical skills. Thus, the model relies on the progressivism philosophy and multiple intelligent theories. In addition, there are some goals have been taking into consideration when designing the model which includes the following: