Week+2+-+School+mathematics+in+today's+world

//**LEARNING ACTIVITY 2.2: School Mathematics in a changing world**//


 * __NEW IDEAS:__**

3 general factors of maths programs: the needs of the subject, the child and society.

> **'The technology principle**' - technology will continue to be important in teaching and learning mathematics, as long as it enhances what s being learned and how it is being taught (NCTM, 2000). > > **'The curriculum principle ' - a curriculum should be focused (on important maths topics and ideas at each grade level), coherent (fits mathematical ideas together in a meaningful way), and well articulated (builds on previous learning) (NCTM, 2000) ** > ** **' ****The teaching principle' - t**o teach maths effectively, teacher must:
 * SUBJECT:**
 * CHILD:


 * know students as learners, and accordingly adjust material to accommodate students' own experiences
 * build lessons based upon prior knowledge, designed to correct misunderstanding and help students to construct their own intricate understanding
 * create a challenging and supportive environment that guides in dissecting and understanding maths
 * encourage students to think, challenge, solve and discuss

> 'The learning principle' - **' mathematical proficiency' being the goal. The importance of understanding - building on personal experience and prior knowledge leads to better understanding, therefore, better maths proficiency. ||  //Social utility: teaching what is needed in occupations.// Once society's mathematical needs were simply book-keepers and accountants. The growth of business and commerce demanded expansion of maths taught. ** > > Much evolution and trying to meet the mathematical needs of society eventually led to the common belief that problem solving skills would be universal to most occupations (occurring in 1980). Eventually the view of problem solving evolved from being a separate component, to a way of learning and using maths. > > 'Society needs a citizenry and a workforce that can solve problems, reason mathematically, process and interpret data, and communicate in a technological world.' (Reyes et al, 2009)
 * SOCIETY:**

__**Changes in maths curriculum**__ //1930 - **Gestalt (field) theory - 'greater emphasis on a planned program to encourage the development of insight and the understanding of relationships, structures, patters, interpretations and principles.' (Reyes et al, 2009). Meaning and learning introduced.**//
 * Pre-C20: Maths taught with the intention of training mental faculties, and mental discipline. "'Exercising' the mind will improve maths." **
 * Early C20:** //connectionism - learning establishes bonds, or connections, between a stimulus and responses (Reyes t al, 2009).// Drills were used to teach maths.
 * 1920 - // incidental learning - children will dictate their own learning, and will learn better without structured teaching. Teacher responsible for addressing mathematical situations when they arise, as well as providing ample opportunity for such a situation to occur. //**

Resources I can use as a teacher: local curriculum, national guidelines, research, history, textbooks, electronic materials, professional organisations, professional development, other teachers.
 * __Psychology and maths:__**
 * 1950 onwards, the importance of the developmental level of the child was noted. They cannot be taught a subject above their developmental ability.
 * Children construct their own knowledge - add their own meaning to new ideas.


 * FAMILIAR IDEAS:**


 * QUESTIONS:**


 * //ADDITIONAL LEARNING:

Identify the 3 goals mentioned in the introduction. Discuss which you believe is most important and why.//** // I consider fostering disposition to be the most significant goal. From my understanding, numeracy is taught, not for the mathematical content, but for the disciplines, skills and procedures learned in the process. While we cannot say that everyone will have the need to use more than basic maths skills, we can with certainty say that persistence, flexibility and the other skills mentioned above will be valuable life-skills to all.
 * To help children make sense of specific mathematical content, including both procedures and concepts.
 * To help children learn how to apply mathematical ideas to solve problems
 * To foster dispositions, such as persistence, flexibility, willingness to learn, and valuing mathematics.

//**Patterns/relationships**//: The area is always (H) x (W) (height multiplied by width) **Art:** To effectively teach maths, teachers must focus on the skills required for maths, rather than the 'doing' maths. Achieving this is an art.
 * Give an example of how maths is a study of the following:**//
 * A** **way of thinking:** A teacher might be looking for a way to arrange her class into groups for an activity. They may use many mathematical methods based on patterns/organising; alphabetizing, ability(?), age, seating. //
 * A language**: Terms used in maths are unique in their meaning. To be coherent in mathematics, users must understand both meaning and correct use of the language specific to maths (Reyes et al, 2009).

//**__LEARNING ACTIVITY 2.3: Record chart - school mathematics in my local context__**
 * Key mathematics content:**


 * Key aspects of the role of technology in maths learning and teaching:

Key principles related to mathematics learning, teaching and assessment:**


 * Key mathematics processes:**
 * Maths provides skills that equip students for life. 'Mathematics and numeracy provide a way of interpreting everyday and practical situations, and provide the basis for many informed personal decisions' (ACARA, 2009). This extends to effectiveness in the workplace, active thinking, interpretation of the world, the use of maths to infer predictions and make decisions.
 * Time, value and importance should be placed upon mathematics, as reflected by the curriculum.
 * 'The learning acquired by students in mathematics contributes to learning in other areas' (ACARA, 2009). This supports the the text by re-iterating the transference of skills used in mathematics to other areas of life such as the work force, decision-making and interpretation of the world (Booker et al, 2009).
 * //'Consideration must be given to the unique characteristics of learners across the years of schooling.' (Booker et al, 2009).// Both content of curriculum and standards of achievement reflect the individual, developmental-age appropriate needs of students.
 * Activities should be engaging, in-depth (as opposed to superficial), and have clear goals. They should offer a range of variety, using technological resources where available.

Was it just me, or did the Victorian curriculum (from [] seem to focus on what needed to be improved within the curriculum? There seemed to be a lot of 'proposing' new, better ideas.

// 1. Unit learning outcome(s) for which this item provides evidence of learning // (type these out in words; do not identify by a number only) //**
 * //PLR
 * Analyse and critique strategies and resources for teaching mathematics in primary classrooms.
 * Demonstrate knowledge of local curriculum documents connected to teaching mathematics.
 * Identify, describe and apply effective teaching strategies for teaching mathematics.
 * Identify, describe and apply effective teaching strategies for teaching mathematics.

2. **Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above** // **(This must be specific in that it includes examples and these examples are explicitly linked to your statements of learning.** **This is not just what 'you' as a person learnt - you need to write about the learning that should have occurred that week, whether you already knew it or not. What were the concepts that those tasks and readings were teaching you? Don't just describe the activity or say what you thought of it - the focus is on the 'learning.' You also need to assume I (as the reader) know nothing - if you use a term (eg. constructivism), you need to say what that is - don't assume I already know.** **What did I learn? Which Learning Outcome did it address? Which activities enabled me to learn this. ** // This week, through the text, I learned the evolution of the needs of maths, and its specific relation to curriculum. This comprised of three areas: the needs of the child, the needs of the subject, and the needs of society. I learned that technology, a constantly-changing society and changes in the way we understand how children think have all advanced the teaching of mathematics.

I also formed a new understanding of several resources available to teachers. These included websites, local and national curriculum documents and technology. Through the learning activites, I discovered two additional online resources: 'Dr. Math' and the 'Illuminations' website, run by the NCTM. The NCTM website offers a range of activities, from kinder through to secondary college, with fun, appealing exercises for students to complete. Dr. Math offers not only answers to several mathematics questions, but also refers students to a live tutor, if required. Access to such a resource was only previously available in the classroom, or through private tutoring.


 * 3.** **How this learning relates to your development as an effective primary mathematics teacher.** //**This is where you must include practical examples for the classroom. How would you teach mathematics based on the learning from the week - this might be strategies, resources or activity ideas?** **You must include references as part of this section to support 'why' these stratgies are effective in teaching mathematics.** **How will I use the learning?** **Why will the learning help in my development as an effective primary mathematics teacher? What references support my claims to the question above?

Now that I understand the needs of a mathematics curriculum, I can also understand the importance of guidelines, and the reasoning behind their creation. For instance, since 1930, teaching mathematics has been largely based upon Gestalt's theories, leading to **' //** greater emphasis on a planned program to encourage the development of insight and the understanding of relationships, structures, patters, interpretations and principles.' (Reyes et al, 2009). This was the introduction of contructivism at its simplest: increasing understanding by introducing meaning to concepts, and forming understanding based on personal experience, and was re-iterated in the curriculum. As a learner, I can review the curriculum and identify the validity of policies, and their relation to the findings of recent research. //

The concept of several mathematical resources was a new one to me, largely because I wasn't aware of the resources regarding mathematics. The introduction and familiarisation of new resources is invaluable to my future as a teacher. If I have access to many different types of activities and ways of imparting knowledge, then I can offer my students richer, more varied lessons. This is supported by the NCTM's teaching principle, which states that the teachers must provide challenging, new activities to promote the development of mathematical skills (NCTM, 2000).

REFERENCES: NCTM illuminations website. dr. math. reyes et al//**