Problems Faced By Algebra And The State Test

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.

Algebra is not an easy subject for many people. It is full of letters, numbers, and rules mixed together to represent real life problems that are hard to swallow for anyone who doesn’t look at the world from the perspective of a mathematician. In his essay, “Wrong Answer: A Case Against Algebra II”, Nicholson Baker addresses this problem and explains why he thinks Algebra II should not be seen as a staple in the education of High school students.

Algebra is a major mathematical strand that has been incorporated across all year levels within the Victorian Curriculum. The many components within and interrelated with algebra and algebraic thinking sets children up, not only for formal algebra in high school, but for life (Reys, et al., 2012). This paper will be addressing some of the main ideas and understandings associated with Algebra. Key skills, strategies and ways of thinking will also be explored along with strategies for teaching the content effectively.

The Common Core State Standards (CCSS) was first implemented in 2010, nine years after I graduated from high school. Although I wasn’t personally affected by the new academic standards, it has a direct impact on the current and future generation of leaders, innovators, and world changers including my future children. The initial purpose of the Common Core Standards is to set high-quality learning goals designed to prepare students to be college and career ready. Given the current controversies surrounding CCSS, studies have shown that although the intent was to benefit students in the long-run it may actually be hindering their mathematical and reading skills. To further explore the arguments behind the Common Core initiative, I will

I was a junior at Brentwood High School, who arrived to the United states from Peru a couple of months ago, and after complaining for three months, Christine Burrows, my guidance counselor, decided to change my Algebra class by a “higher” level math.

Since a public school district’s success is determined by state and national assessment, officials in school systems across the country have sought to make changes to effectively address the academic deficits of students. A push in education over the past couple decades has been the race to Calculus and the belief that this path is necessary for a student to succeed in advanced math courses in college. Although there has been a dramatic increase in the number of students in high school Calculus, enrollment in Calculus 2 at college has remained relatively unchanged for the last two decades (Bressoud, 2004; 2009). Many students who have taken Calculus in high school are arriving unprepared for Calculus in college (Bressoud, 2007).

This program is appropriate in a diverse, 4th grade general education classroom. The modules are made up of “Topics” and “Lessons” that are aligned to Common Core State Standards (CCSS). Each module provides the foundational standards needed for the lessons (i.e. CCSS from the previous grade), as well as the focus grade level standards. The first module introduces concepts which are then spiraled within the next module’s focus. While the modules are thematic and based on each mathematics domain (base ten numbers, geometry, fractions, data, algebraic thinking), some standards are seen across topics and lessons. Each lesson has allocated time to four major components: fluency practice, concept development, application problems, and student debrief.

The new Common Core State Standards for Mathematics bring a new opportunity to the classrooms of the United States that many people view as a controversial. According to the NCTM (2013) “The Common Core State Standards offer a foundation for the development of more rigorous, focused, and coherent mathematics curricula, instruction, and assessments that promote conceptual understanding and reasoning as well as skill fluency” (par. 1). While some people believe that the Common Core State Standards may hinder progress in the classroom for many reasons including too much government control, teaching to the test, an excessive focus on language arts and math, and wasted resources, others agree with the NCTM statement about that claims the standards help increase conceptual understanding, reasoning, and skill fluency.

At New Bern High School, Charlie Bernthal, a freshman, sits in a class room instructed by Common Core standards. It will take one of Charlie’s teachers six minutes to demonstrate the various methods to complete a simple multiplication problem, such as 63 x 24. Students are taught to use arrays, lattice, partial product methods, and eventually the traditional U.S. customary method. The Common Core standards happen to be a big discussion point during this year’s election. People have many strong opinions when it comes to the Common Core State Standards, but researchers and institutions express reasons why teachers and schools should not use Common Core to instruct America’s youth. Schools and teachers should not teach by Common Core standards because these standards are detrimental to our children.

I have had the pleasure of teaching Ally in class for three years; in Advanced Geometry as an 8th grader, Pre-Calculus as a sophomore, and currently as a junior in AP Calculus. In 8th grade, Ally chose to arrive at school an hour earlier in order to take Advanced Geometry at the high school. Even at that young age she knew she wanted to take advanced math classes and push herself academically. Ally's greatest strength in class is her inquiring attitude. She has an unique ability to analyze and reflect on the problem-solving process. While solving complex mathematics problems, she will refine and improve her problem-solving strategy to obtain the correct solution. When I give her exams back, Ally critically examines her mistakes to learn from them often sharing her findings with her peers.

-The student will be able to evaluate, and analyze the given information to solve mathematical word problems.

Katherine Lucadamo, author of the article “Back off parents: it’s not your job to teach Common Core math when helping with homework”, has a daughter in first grade. One day while helping her solve a math problem, she explains, Katherine was unable to do number bonds. Her daughter’s teacher explained that three circles form a pyramid and the bottom stack are for addition or subtraction while the top is for the total. Katherine thought that this math, which she was unable to figure out, is too confusing for a six year old. Katherine is not alone in this confusion, as parents all across America are having trouble helping their kids with homework after Common Core Math was introduced.

Question 16 of the EYMCT identified my weakness in Number and Algebra sub-strand patterns and numbers. Even with tutoring during high school I was unable to achieve a deep understanding in this area of mathematics (see appendix A). Given the test results, these challenges that I faced within this area of mathematics has continued into adulthood. Even after reviewing Question 16, I struggle to see the structure of the pattern and how “CC” comes next in the pattern “AA BB AA CC AA DD BB CC BB DD”. As a preservice educator, this lack of confidence in and a shallow understanding on algebraic patterns can negatively impact on student’s achievements in other areas of mathematics. This is because patterns in algebra can be linked to other areas of

The lack of adopted curriculum also means that most, if not all, teachers are supplementing both materials and instructional routines. These students need to pass the state-mandated Smarter Balanced Assessment (SBA) which requires completion of a problem-solving performance task. Students need to know which operation(s) to use (addition, subtraction, multiplication, and/or division) and how to apply them appropriately. This problem has

Computer Algebra Systems (CAS) were first introduced in the early 1970s on large frame computers and are now accessible on a hand held CAS calculator that is increasing in popularity and affordability for high school students (Kendal, 2006). The CAS calculator is a multi-representational too with symbolic, graphical and numeric capabilities and a large variety of procedural skills that include calculus, drawing graphs, and the execution of numerical, vector, matrix, and statistical calculations (Zbiek, Heid & Hirsch, 2009). The CAS calculator is a powerful dynamic tool that offers opportunities of learning new concepts and experiences and allows teachers to use the CAS to help students focus on either a more targeted or a global view of their work with symbolic representations, depending on the instructional goal (Zbiek, Heid & Hirsch, 2009). Bert Waits, co‐founder of T3 (Teachers Teaching with Technology) mentioned that graphing calculator is a great pedagogical tool as it offers multi‐representational approaches in teaching and learning of mathematics (Parrot & Eu, 2014).