Teaching and Learning 'Rate of Change'' (Slope) in Senior Secondary Schools in Australia

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 stage 4 mathematics Unit of Work (UoW) “Unit 10 Measurement, Length, Perimeter and Area” implements an array of concepts to aid the students to learn multidimensional mathematics through applying an Aboriginal perspective. These concepts that are outlined are the choice of and conversion between metric units, establishing and using formulae to solve perimeter and areas of squares, rectangles and triangles, utilising pi and solving perimeters of circles and solving problems using perimeter, area and circumference. Although the unit mentions the importance of the use the Mathematics problem solving there is a majority of content that is missing on the cultural aspect of mathematics as it highlights the prominent use of one-dimensional Mathematics.

I believe Math is learned by doing the problems and doing the homework. The problems help you learn the formulas you need to know, to help with problem solving. I have learned from my own personal experience that you must keep up with the Instructor: attend class, read the text and do homework every day. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep trouble.

He has many publications, including the authorship, co-authorship, or editorship of textbooks in middle grades and high school mathematics, six professional books and eight book chapters. Dr. Stiff is a textbook author for the Houghton Mifflin Harcourt Publishing Company and McDougal Littell. ''Houghton Mifflin Math'' is an elementary textbook series, K-6; and McDougal Littell's titles, such as Math Course 1Algebra 1, Geometry, and Algebra 2 which is usually middle and high school math textbooks. (Lee V. Stiff (8301), 1999) This is a list of some current textbooks that was credited by Lee Stiff: Developing Mathematical Reasoning in Grades K-12, Geometry: Reasoning, Applying and Measuring and Heath Algebra1: An Integrated

And it connects with the Australian Curriculum areas: Create symmetrical patterns, pictures and shapes with or without digital technologies. The Storytelling strategy engages all students in listening and promotes their imagination, emotions and critical thinking skills while learning the main concept of math. The class discussion along with questioning strategy throughout the lesson promotes students’ exploratory conversations and shared experiences on mathematics. The main theme of this lesson is to enable students to understand Aboriginal symbols in the painting and reinforce the relation of the mathematical concepts behind the symbols.

In the article, “13 Rules That Expire,” by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty, the three authors discuss thirteen of the most commonly used tricks, tips, and strategies that do not promote a full understanding of mathematics. Furthermore, this promotion of shortcuts and alternatives that are commonly steering children to misunderstandings as they grow and expand their knowledge in a higher level atmosphere. These strategies are that discussed in the article are taught in elementary and middle school levels. However, once these rules are taught and established they tend to expire around grade seven and up when children start learning complex multistep problems. The overall content of the article is accurate when

In Unit 1, many topics and concepts about motion were covered. We started out with the basic ideas of motion into much harder ideas. Before that though, we learned how to read graphs to determine their mathematical expression and the keywords needed to understand motion. Such words includes position, velocity, acceleration, displacement, speed, instantaneous velocity, etc. Building off of that idea, we went on learning how to draw and describe acceleration arrows, motion maps, x, and v, and graphs based on the given scenario. Furthermore, we also learned how to calculate position and slope. We know that to calculate the position, the equation is position= (velocity) (time) + initial position and that the slope is the change in position over

Geometry and Algebra are so crucial to the development of the world it is taught to every public high school in the United States, around 14.8 million teenagers each year (National Center for Education Statistics). Mathematics is the engine powering our world; our stocks, economy, technology, and science are all based off from math. Math is our universal and definite language “I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings.” (Rene Descartes, 1637).

from. For example, students may know how to graph an equation on a calculator and

Renee is creating a slope graph using computer software program. That involves using mathematical skills like algebra.

Before this adventure in slope, I know I have never said to anyone “slope is the most basic rate of change”. Basic may not be the appropriate word, but slope is typically a student’s first introduction to rate of change and it is somewhat simple, since the slope is the constant rate of change for a linear function. Where am I going with this you may wonder? Semester after semester I have introduced, reviewed, and examined slope with students, but I may have also caused a disconnect in students’ conceptualizations of slope. I never said, “slope is the most basic rate of change”.

When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower transformation

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

Markworth (2012) suggests ways students can learn algebraic concepts and geometric patterns by developing an understanding of functional thinking. Growing patterns are a useful counting method that allows students to engage with algebra. Geometric growing patterns best support student’s ability to develop functional thinking which is essential. This article outlines three teaching strategies for using geometric growing patterns, these are:

Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop.