The need to offer a more effective mathematics curriculum is critical for Students. In development and implementation of the Maths curriculum, it stands to reason that if the current program aspires to increase unit requirements and advanced mathematical skill proficiency for graduation, the program must specifically attend to content requirements at the primary level to effectuate a significant and lasting impact in the lifespan of student academic performance (ACARA, 2013)
Planning For Diagnostic Assessment
According to Cavanaugh, (2006) research documenting that the number of mathematics topics covered prior to secondary education courses is positively correlated to mathematics achievement while the number of new topics presented at the secondary academic level is negatively correlated to mathematics achievement. Therefore, the math curriculum must provide students with opportunities to learn and acquire mastery with regard to math at an early age.
The focus must be placed on specific problems in skill acquisition in mathematics and using acquired skills to the foundations necessary for understanding higher level math. These foundations can only be built with a mathematics program that teaches concepts, skills and problem-solving (Daro, 2006).
In order to best facilitate such a focus, teachers must properly assess students at each stage of the critical learning process. The present study presents the optimum procedure for assessment of students. Two students were selected for this study of convenience, and their parents were advised of the study, its purpose, and the importance of ongoing diagnostic assessment in the learning process. For optimal result, the engagement of the parent in the process effectuates a more accurate portrayal of the student, and further strengthens the parent-teacher partnership in the educational endeavors of the child.
For the purpose of this study, two students were selected for assessment and the development of student-specific learning plans. With the approval and guidance of supervising instructors and the full disclosure and cooperation of the parents of the respective children, all necessary and appropriate documentation has been completed and the parents and participating children have been fully advised of the purpose of these assessments. All documents will be kept under lock and key when not being used directly by this writer to maintain the confidentiality of the children. All documentation regarding the informed consent process, individual student assessments, and assessor observations have been recorded and appear in the appendices of this paper.
The participating students were assessed based upon their grade level expectations per the ACARA (2013) curriculum guide. The students were timed on each exercise and carefully observed. After careful assessment and evaluation of the assessments of each respective student, individualized learning plans were constructed, based on the specific needs that were identified during the assessment process. Consideration was also given as to the concerns of parents in the informed consent process preceding the assessments. Sample lesson plans appear in the appendices of this report that are reflective of the types of exercises that are recommended for each of the participants.
The purpose of this paper is to discuss and apply six guiding principles related to equity, curriculum, teaching, learning, assessment and technology, and identifies content and process standards explaining what students should know and be able to accomplish at various levels of the learning process. The content standards are comprised of content specific applications related to numbers, operations, algebra, geometry, measurement and data synthesis (ACARA, 2013; Van De Walle, Karp and Bay-Williams, 2010). The Maths curriculum is organized around the areas of problem solving, reasoning and building upon acquired skills to continue the learning process (ACARA, 2013).
Thompson, (1999) postulates the model of mental calculation, which addresses facts, understandings, flexible mental strategies, leading to development of skills and positive attitudes about learning the subject matter. To summarize, it has been argued that a minimum requirement for children to be successful. According to Thompson, mental calculators represent the development of a secure knowledge of number facts; (Thompson, 1999) and a good understanding of the number system including how the system works and which operations are permissible, so that known number facts can be combined using appropriate operations to work out other facts. Mental Mathematics also prioritize the ability to accurately demonstrate the skills underpinned by acquired understandings, leading to having the confidence to use what they know in their own way to find solutions (Thompson, 1999).
The teacher’s job is to ensure that these aspects form an important part of their teaching. According to Thompson, (1999) this entails a good knowledge of the common mental strategies that children use so that teachers can understand their own children’s methods and support learners in refining these strategies.
Mental Computation Strategies
Mastery of basic math operations can help students develop more sophisticated methods. To this end, Teachers must be attuned to their own teaching strategies for developing children’s attitudes in terms of calculation, particularly with respect to their pupils’ confidence in using methods of their own preference. (Thompson, 1999) Therefore, teachers can create a suitable classroom ethos where students will be confidently prepared to take risks.
Teaching Mental Maths
In order to effectuate successful learning with effective strategies for mental calculation for all children, the Maths teacher should ensure that they do not emphasize the efficiency aspect to such an extent that children reject a method they understand in favor of a more efficient one that they do not understand (Thompson, 1999). One important aim of the National Numeracy Strategy, launched in 1999 asserted the urgency for children to be confident with and competent at mental addition and subtraction 01 any two-digit numbers before they left primary school (Thompson, 1999).
All students must have an opportunity to learn new mathematics. It must be established that all students potentially possess the capacity to learn more mathematics that include new processes that build on existing skill sets. (ACARA, 2013) While advancements and changes in technology have prioritized the instructional importance mathematics concepts, learning environments can be made more student-friendly through enhanced learning tools that include technology, such as computerized programs that offer context-specific skill building lessons for each skill that requires mastery at all levels of the learning process related to mathematics. Given that the study of mathematics is a meaningful process, educators must concern themselves with developing positive engagement and interaction that is student specific, while taking into account that prior experiences and learning mastery must be successful (ACARA, 2013).
The fundamental focus area requires the assessment of basic skills with numbers, as students must learn how to address precise definitions and rules while mastering concepts. The skill must be developed in solving simple equations with progressive reasoning in the problem solving process (CTME, 2006). The Maths program assumes that fluency in mathematical study is both foundational and somewhat memorized, because this study demands automatic recall of certain procedures and algorithms (ACARA, 2013). Therefore, the comprehension of basic algorithms of whole number arithmetic is critical. In addition, the development of a sound understanding of the numeric meaning of fractions is essential in the primary grades when combined with multiplication and division operations. Follow up exercises should first concentrate on reinforcement of basic operational procedures (Reys, 2009). Integrative exercises should then be included as the student develops confidence in their execution of the operations.
The Maths curriculum posits that instructors at all levels must emphasize the use of “real-world” contexts for teaching mathematics and placing a continued focus on progressive skill development in mathematical ideas (Sparrow, 1994; Thompson, 1999). To this end, mathematics should be taught using multiple strategies (ACARA, 2013). Teachers and teaching staff should retain responsibility for selecting appropriate strategies for mastery in specific content area concept (Sparrow, 1996). Therefore, teachers must not only understand all underlying meaning and justifications for mathematical operations from basic addition to complex procedures such as Calculus, but they must also present appropriate curricula that inspires the same understanding for all students at each stage of the developmental learning process (Van De Walle, Karp and Bay-Williams, 2010).
With regard to each student, a personalized focus on practice in a variety of activities should serve to enhance the student’s confidence while preparing the student for progressive and more complex mathematical computation (Van De Valle, Karp and Bay-Williams, 2010). While both students exhibited varied levels of anxiety in the assessment process, both would benefit by practice exercises geared toward their interest. Moreover, both the students would benefit by positive reinforcement with the completion of exercises. Any weaknesses in mathematical operation or reasoning can be easily facilitated with reinforcement exercises (Reys, 2009).
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