Mathematics and Logic - Skill and Concept Development

Introduction to Section Content + General Advice

See too the general advice on helping your child or teenager in mathematics below.

1. Speaking Skills suggests how to improve the speaking and listening skills of your child.
   

2. Reading & Writing offers ideas for the development of these skills.
   

3. Preparing for science -Teaching a boy or girl to cook or to follow any multi-step method precisely, in a repeatable and reproducible manner, will help in science and all area of work and study.
   

4. Learning Takes Time and Effort: Four Things for a Student to Know. Quote in full of an article from Speaking of Learning that refers back to words at this site, no longer online.
   

5. Patience Please. Reflects the inductive idea that learning takes time. If you see a difficulty, you need to identify the source and retreat before it in order to practice skills that restore confidence and then to practice skills that remove the source of the difficulty. Teaching, tutoring or parenting takes time and patience. Good luck. Nothing is certain.
   

6. Who is in Charge? For better or worse, you the parent or guardian may be the first and longest term instructor of your child. Do your best
   
   Parents and teachers need to say no for small things of little consequence to build and maintain authority to say no for larger matters. Parental authority: ; use it or lose it.
   

7. Student Motivation Here a discussion of the challenge. Not the solution. ;
   
   Students with parents who say mathematics mastery is important, or education in general is important, will ; often have more goals, more will and more staying power in school and college - no guarantees here -but is part of the solution.
   

8. Talk to Your Child or Teen. For many, those without learning difficulties, the will to learn is often more important than ability. Encourage the will. ; That is part of the solution.
   

9. Discipline in Schools: Streaming by Student Cooperation. Societies that want quality education will preserve the authority of teachers in the classroom, while providing safeguards so that the that teachers do not abuse that authority. In the first instance, students may be streamed by their willingness to cooperate with teachers, and then by their academic destination. People with good education will not want to go into classrooms if [A.] student disrespect is a constant danger; and [B] present-day course design in their discipline areas is inconsistent and irrational according to their previous training in the discipline. Uniform standards in education are mixed blessing. While in the first instance they raise standards, over time central planning or bureaucratization may lead to those standards being lowered. In large enough regions, different school systems should develop their own standards, with multiple independent centers for course and curriculum design, each trying to offer a different design, each staff in a way that rejuvenation is continuous or mass retirement in one is not simultaneous with mass retirerment in another.

10. Work & Study Ends, Values and Methods. These appear to be missing in schools.
    

11. Parents Need to Follow & Supervise the Education of their Child or Teen.
    
    If your child falls behind, provide extra help during the school year or during summer vacations. Ask your school for a list of observable skills that it and you should be verify. If there is no list, form one alone or with other parents. If ; there is no list of observable skills, your child school system has no idea where it is heading. It is lost. ; ;
    

General Advice For Mathematics Skill Development

In general, explain to your child or teenager that skills in mathematics and other subjects need to be seen to believed. In arithmetic and beyond, talk about the need to do and record work step by step, so that each step can be checked as done or later. Emphasize too the domino effects of errors, that is, how an error in one step leads all or most following steps to be in error as well. If local textbooks are too hard for you to follow then your child or teenager will have difficulty as well.

For children or preteens ages 3+ to 12 years of aged learning mathematics, use parent friendly, Work Booklets to build or rebuild skills and confidence. Emphasize mastery arithmetic and geometry has value in adult and daily life. say this mastering is part of growing up, like learning to read exactly what is meant, and to write exactly what they mean.

For children or teenagers, ages 12 and up, site material may help you check and develop skills in stronger ways that seen in school. Mastery of site material unfortunately requires adult level patience and reading abilities that most students, except for the gifted and talented do not have. So you or a tutor will have to give less gifted learners ages 13 to 19, skills and concepts to master in parallel to the skills and concepts that teachers provide in school.

In the early years of secondary school, your teenager may need to be tutored to prepare them for course test and finals, besides following site steps as site material and your local school may follow two different paths. But within a year or two of effort, site steps, ends and values for skill development should help your child do well in school. But again there is no guarantee your child will be able to follow the site program - that remains to be seen. So you have explore site material or rely on the judgement of others to decide what route to follow. Good luck.

If you are lucky, your local school does not follow the new-age, constructivist approach to education. In it,

• Children are told the best way to learn a subject is from discovery and from their personal experience.
• Teachers are also told that true knowledge for each student is a private matter, a product of their reflection on their personal experience, a product that can not be reliably tested nor corrected in class and on final examinations. in class or in final examinations.
• Teachers are told to introduce idea indirectly, so that students may discover them for themselves. In this, various kinds of problems and challenges are to be given to set the stage for this self-instruction.

Teachers are further told that giving students skills and concepts to master is a substandard form of instruction. At the same time, school authorities and parents like you want their children and teenages to do well on final examinations. Such final examinations test student mastery of skills and concepts that used to be given directly instead of through hints. There is a contradiction between theories that hold students should be taught indirectly, and the practice of wanting students to do well on tests and final examinations of skills and concepts that previous educational theories and practices tried to develop directly. That being said, site material stems from the observation of gaps and steps too large or missing in the direct explanation of key skills and concepts. In particular, site material aims to remedy the foregoing by providing teachers and tutors, and the gifted or talented, clear and direct explanations likely to ease, avoid and even explain for common fears and difficulties.

Clear How-TOs, ends and values for the direct explanation of given skills and concepts need to be well-known and well-documented before instructors, well-versed or not in mathematics and logic, are called upon to develop skills and concepts indirectly. Otherwise, indirect instruction will simple compound the shortcomings of direct instruction in skill and concepts development. The problem with constructivism is that moves the focus of education away from worldly concerns.

This viewpoint of constructivist-led indirect instruction stems from the perspective that arts and disciplines at home, in school and the workplace require an observable and verifiable mastery of visible and hence verifiable skills. Skills and abilities in many arts and discipline need to be seen to be shared, to be well-defined and believed. In particular, skill in cooking at home and in a restaurant may involve some thought or reflection that we cannot see, but that skill needs to be seen to believe. In general, we do not want cooks who think, we want cooks that can do. Likewise, we want cloths designers and makers, plumbers, electricians, interior decorators, construction workers, factory workers, engineers, book-keepers, accountants, scientists and mathematicians who not only think about what needs to be done in the privacy of their own minds, but also display skill in ways that can be seen and judged. The format of that display may vary from discipline to discipline.

In mathematics itself, practical concerns suggest the following ends and values. Instruction should first serve on the development of basic skills and concepts with of service in daily and adult life. Second, it should serve the needs of pre-college or precalculus occupuations. Finally, it should serve the needs of calculus and precollege courses in science and technology. Calculus is required for college level studies in accounting, commerce, engineering, science, technology, mathematics and mathematics education. Here serving the first end may serve the next two, and serving the second may serve the last. Further, there is no harm in college bound students seeing skill and concepts for adult and daily life, and for precollege work destinations as a parachute or safety net as there is no guarantee that their college studies will succeeed. Mastery of logic, awareness of the domino effect of errors, and awareness of how many later skills and concepts depend on earliers could provide further ends and VALUES to guide both learning and teaching.

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