Mathematical Practice Standards and Tools in Mathematics Education

This assignment delves into the realm of mathematical practice standards, emphasizing the strategic use of tools in problem-solving across different educational levels. It highlights the progression of tools from basic instruments like rulers and pencils in elementary school to more advanced technologies such as graphical calculators and computer algebra systems in higher grades. The document stresses the importance of teachers guiding students in selecting the appropriate tools and fostering critical thinking. Furthermore, it explores the application of mathematical knowledge in solving real-life challenges, such as financial planning, and underscores the need for developing reliable mathematical models by considering all relevant variables. The conclusion reinforces the significance of mathematical proficiency in everyday life and the essential qualities that students should possess to excel in mathematics, providing valuable insights for educators to cultivate future mathematicians.

Running head: Mathematical Practice Standards
Mathematics Assignment
Institution Name
Student Name

Mathematical Practice Standards
From the document presented it has been approved that a proficient mathematical
student makes strategic use of necessary tools effectively. During the lower stage, students
may make use of simple tools such as rulers and pencils to solve arithmetic issues. It is
essential for the mathematician to be knowledgeable on some instruments that are applicable
in mathematics computations. The number of the tools increase as the student progresses to
higher levels. Precisely, in the in the elementary level mathematics students do use simple
tools in their solutions, the use of papers, pencils are rulers are frequent as the student slowly
learn to make use of the instruments to assist them to evaluate a mathematics issue. The tools
are useful in presenting diagrammatic views which help the students conclude.
As the students' progress to the junior through to senior high school levels more
complicated but efficient tools are brought to their disposal. Items like the graphical
calculators can be used to analyze functions and their solutions. The tools become more
complicated at the college level than in the junior levels. At this point, the mathematics
students are exposed to a dynamic set of tools. This ranges from spreadsheets, computer
algebra systems, dynamic geometry software as well as statistical packages. The challenge
here is for the student to identify which tool can best fit their problem. For a mathematics
student to be prolific, it is therefore mandatory that he/she assess all the tools available and
select the best that gives the most efficient solution. Also, technological tools can enable
exploration and a deeper understanding of mathematical concepts (Stigler, 2000).
The document highlights the need for mathematics student to apply practical tools
when solving mathematics problems. A confusion which arises is the actual role of the
mathematics teachers when it comes to assisting students to select the necessary tools.
Teachers analyze students work as well as respond to their methods of designing solution but
when the students are left to solve an issue what role do the teachers play in their choice of
mathematics instrument? Occasionally selection of tools for tackling mathematics issues do
entail a level of critical thinking on the part of the student being that teachers are not always
available when a student is addressing the problems, how are their activities responsible to
the students' dimension of thinking?
In one of the post, the student indicated the use of mathematical knowledge in solving
everyday life challenges as one of the attributes of proficient mathematical students. From the
post, the way the issue has been illustrated is to indicate and I wish to appreciate it. The
student has given examples of the style student can use simple models to predict and plan for
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Mathematical Practice Standards
their daily expenditure as one area in which mathematics models assist in solving daily life
challenges. From the post, the student is concerned with how to ensure the reliability of the
models and improve the quality of decisions reached via the modeling criteria.
In response to the students' shortcomings when it comes to catering for the reliability
of mathematical models all start by stating that models in ordinary cases lead to projections
other than giving actual future occurrence. As a way of ensuring that the student use of
models provides a realistic approximation with its mandatory to consider all the variables
involved. The student will, therefore, have to develop sensible reasoning from the task and
make a quantitative view of it before beginning to develop a solution. In cases like the
businesses estimation of costs and revenues, the accountants and cost analysts combine to
identify the all the variables of concern. In this case, the past information associated with
revenues, expenses and costs are all brought together, and a model is developed which covers
all the areas. If this is added to the use of an appropriate mathematical tool, then the
mathematics technique will be instrumental in solving the current issue (Furner, 2007).
In conclusion, mathematical knowledge is a vital tool in solving the everyday
challenges that everyone faces in their daily activities. As a teacher, the standards highlighted
about practicing mathematics indicate some of the essential qualities that students ought to
have if they are to excel in math. The issues have been beneficial as they direct the attention
of the teacher to some of the areas that need to be attentively covered to mold the student into
mathematics veterans.
References
Furner, J. M. (2007). The Mathematics and Science Integration Argument: A Stand for Teacher
Education. Eurasia Journal of Mathematics, Science & Technology Education.
Stigler, J. H. (2000). A proposal for improving classroom teaching: Lessons from the TIMSS video
study. The Elementary School Journal, 3-20.
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