Success in Mathematics

1) Summary Statement

In order to be a successful learner in the discipline of mathematics, a student must possess various skills, dispositions and areas of knowledge. A student must be able to solve varying problems, communicate their reasoning and explanation, make connections to previous knowledge and real-life experience, use logic and reasoning in the disciplinary activities, use and create symbolic mathematical representations to support ideas and effectively utilize technology to enhance mathematical applications.

In addition to possessing certain skills, successful students must also have the right attitude towards math to gain the most relevant and valuable experience with work in the discipline. These attitudes and dispositions are also reflective of teaching practices and therefore directly apply to both learner and instructor. The students must feel a genuine excitement or interest in activities that help them to learn the mathematical concepts, rather than memorize procedures. These activities should evoke interest and engagement based on meaningful and life relevant problems. Students must possess attitudes that will lend themselves easily towards the necessary collaborative and cooperative nature of maximizing learning in math. Dispositions such as respect, high self expectations and motivation to advance are also valuable, but in summation it should be noted that these attitudes and dispositions are not intrinsic in all students of mathematics and therefore depend a lot on the teacher’s influence.

Finally, and at the core of the discipline, students must acquire knowledge principles from their career as pupils of mathematics. Essentially, the students must know number sense and operations, principles of estimation, geometry, measurement, patterns, relationships, procedures, probabilities, statistics and discrete mathematics.

With that, the knowledge, skills and dispositions that make up the components of a successful learner of mathematics depend on a highly qualified and enthusiastic teacher who shares the same qualities and characteristics as the standards envision for the student who will study from them.

2) How do the NJCCCS meet diverse student populations?

- Ethnicity
o Math is cross-cultural and multi-lingual in nature
- Special Needs
o Math is recursive, representative, symbolic and uses algorithms
- Multiple Intelligences
o Math is collaborative, individual, visual, concrete, abstract, creative and found everywhere in daily life

3) How do the NJCCCS not meet diverse student populations?

Since mathematical concepts build upon one another, if the student does not actually learn previous skills it is difficult for them to advance

The NJCCCS do not take into account teacher fallibility or external factors that might prevent their embracing and progress in mathematics

There is an inherent assumption that all areas of math from the previous year were taught and mastered by the student, which is not always true because of time constraints, absences or other struggles – forcing students to play a constant game of ‘catch up’ that would hinder the growth of necessary attitudes and dispositions towards the discipline of mathematics

4) What do they imply is of value? (in reaction to teaching and learning)

The implicit value necessary in the teaching and learning of this discipline, mathematics, is essentially the enthusiasm, excitement, engagement and relevance of math to the life experience. Logic and reason, two tenets of philosophy and the basis of all coherent thinking, are the ultimate goal of mathematical studies.

Knowledge, Skills and Dispositions

The vision of the mathematics standards is focused on achieving one crucial goal:

To enable ALL of New Jersey’s children to acquire the mathematical skills, understandings and attitudes that they will need to be successful in their careers and daily lives.

Big Ideas:

 Number Sense
 Numerical Operations
 Estimation
 Geometric Properties
 Transforming Shapes
 Coordinate Geometry
 Units of Measurement
 Measuring Geometric Objects
 Patterns
 Functions and Relationships
 Modeling
 Procedures
 Data Analysis (Statistics)
 Probability
 Discrete Mathematics – Systematic Listing and Counting
 Discrete Mathematics – Vertex-Edge Graphs and Algorithims





Skills:

 Problem Solving
 Communication
 Connections
 Reasoning
 Representations
 Technology






Dispositions:

 Students are excited by and interested in their activities.
 Students learn important mathematical concepts rather than memorizing and practicing procedures.
 Students pose and solve meaningful problems.
 Students work together to learn mathematics.
 Students write and talk about mathematics every day.
 Students use calculators and computers as important tools of learning.
 Students foster respect for the power of mathematics.
 Students set high expectations for themselves.
 Students go beyond the standards to advance their understanding of mathematics.

Analysis of NJCCCS - Math (Presentation Posting)

http://www.nytimes.com/2006/11/14/education/14math.html

http://www.aft.org/pubs-reports/american_educator/issues/spring2008/index.htm

“The best laid plans of mice and men often go awry.”

Twenty years ago, the nation began standard based reform as an idea to improve schooling for instructors and pupils alike. The standards established what students should know and be able to do and were supposed to offer guidance to teachers, curriculum writers and educational administration. The state standards, upon review, are all too much vague, complex and lengthy. The intentions are good, but the fact that many teachers are forced to focus their time to ‘teach to the test’ releases the accountability that all the standards are met at each grade level. This leads to gaps and repetitions in content for the students and creates problems for the educators in the child’s future. Additionally, two experts from American Educator journal state that, “State tests and state content standards don’t always match up.” Now that we have standards in place, it’s time to redo them so that they are clear and specific and a more reasonable length. In an attempt to flesh out the state standards in Math, our group has examined the nature and purpose of the essential information that will help guide teachers through the understanding process.

“Keep it simple, stupid.”

The standards help curriculum writers because they act as a springboard for developmentally appropriate instruction that builds upon prior learning. They assist teachers in determining what should be taught in the classes they are assigned. Standards hone in on specific items of knowledge and skills that successful students should master throughout the year’s lessons. In an attempt to create a list of concepts students must understand and value in order to advance, the standards became unclear and tried to encompass everything at every level. Overwhelmed teachers have fallen prey to the complexity of standards and opt for relying on the 800 page back breaking textbooks of the district mandated curriculum to “cover” the material instead of offering students a deeper understanding of the discipline. Identifying strong core standards and limiting the length and convoluted language will help give educators and curriculum developers the necessary foundation for a content rich, sequenced curriculum with aligned assessments.

“After all, what is more central to schooling than those things that we, as a society, have chosen to pass on to our children?”

The Third International Mathematics and Science Study (TIMSS) has confirmed that student performance is directly related to the nature of curricular expectations. Through their research, it has revealed that the focus, rigor and coherence of Math standards are of utmost importance. These three aspects are the basis of strong Math education. Unfortunately, the attempt to focus has been lost through creating a ‘to-do’ list of too many topics for coverage instead of mastering fewer topics during a given school year. This unintentional reversal of purpose leads to students who don’t have a firm grasp of the concepts they need to build upon in the later years. Administrators and standards demand rigor in the classroom, but that falls short when students need remedial teaching of basic concepts in order to process more advanced and abstract Mathematical thinking. Finally, coherence is the most important part of well-developed Math standards. The inherent weakness of our Math framework is that there is too much covered at each grade level, some may even be called developmentally inappropriate, and the breakdown begins a domino effect of struggling students at each level – preventing proper advancement.

“Everybody else is doing it, why can’t we?”

While the question of why American students miss the mark on Mathematics assessments worldwide, one has to consider whether it is the diversity and poverty of our students or our standards before placing the blame. Math curriculum does promote varied skills, concepts and activities to reach a variety of students without sacrificing individualism but it has not fostered continued growth in many students. Because standards are open to interpretation by the teacher planning the lesson there is also great variety of content taught among courses with the same level and title. This variability in course content and the plentiful amount of requisite standards creates a set of artificial tracks in the curriculum that have negative ramifications on Mathematical literacy. While other, more successful, countries focus on fewer topics, they also demand that Math is taught in a meaningful way. Curriculum writers must delineate what is important to teach and articulate those choices through the standards, textbooks and assessments of the discipline.

“Through rose colored glasses…”

The most valued aspect of teaching and learning that the standards imply is that of student and teacher dispositions. The attitudes towards Math of both pupil and instructor help to foster the strong relationship necessary to understand the essence of Mathematical thinking and its relevance to everyone’s life. It may be easy to see how a student of the discipline can break their bond with Mathematics when they feel frustrated or confused due to the standards pushing too many demands when teachers are unable to meet and address all concepts for student mastery.

“Less is more.”

Ultimately, the review of the New Jersey Math standards has brought to light the fact that the political machine’s, controlling standards development, eyes are larger than the students’ academic stomach. We have too much on our standards plate, and the abundant cornucopia of knowledge and skills that teachers must pass down the table to their students each year never truly makes it to the other end. Students are being left behind due to superficial ‘coverage’ of Mathematical concepts instead of truly digesting what is most important to learn. This starts the end of what was once a beautiful relationship between student and discipline, leading to feelings of distaste for Math and eventually avoidance of the subject altogether. Overextending teachers and students result in the reversal of what the standards’ original goal was: The student’s internal motivation to advance. In order for the standards to improve, states and districts must bring mathematicians into the standards setting process and push the politics out.

Calling for Clear, Specific Content (American Educator, Spring 2008)

These are some problems that the editors of American Educator magazine have published in reference to the gaping holes in state standards:

~ Professional development is too often about pedagogical fads.

~ Too many districts don't even try to flesh out the state standards, leaving teachers to face that challenge on their own.

~ Students, especially those who change schools frequently, end up with gaps and repetitions - never doing an experiment with seeds, for example, but having Charlotte's Web read to them three times.

~ Textbook developers try to "cover" the standards by creating 800-page back breakers.

~ Teachers' (and administrators') guesses as to what will be on the state assessment often end up driving instruction.