FORMULAS FOR DYNAMICS, ACOUSTICS AND VIBRATION

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Teaching Number Knowledge

Knowledge Activities

The activities in this book, if modified appropriately to meet the needs of students, can be used as whole-class warm-ups at the beginning of a lesson. Many of the activities can also be used with individuals and groups of students to build and maintain key knowledge. Some items of knowledge are critical enablers in helping students make strategy stage transitions. These key items of knowledge are listed in the planning formats provided in Book 3: Getting Started under the heading of “Key Knowledge Required”. It is also important that students are given opportunities to enhance their knowledge while they are developing strategies. Suitable knowledge outcomes for each stage and operational domain are included in the planning formats under the heading of “Knowledge Being Developed”. The following key is used in each of the teaching numeracy books. Shading indicates which stage or stages the given activity is most appropriate for. Many activities, given suggested modifications, are suitable for a range of stages. Note that CA, “Counting All”, refers to all three counting from one stages. Download

Single and Multivariable Calculus

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. If you distribute this work or a derivative, include the history of the document. This text was initially written by David Guichard. 

The single variable material in chapters 1–9 is a modification and expansion of notes written by Neal Koblitz at the University of Washington, who generously gave permission to use, modify, and distribute his work. 

New material has been added, and old material has been modified, so some portions now bear little resemblance to the original. 

The book includes some exercises and examples from Elementary Calculus: An Approach Using Infinitesimals, by H. Jerome Keisler, available at http://www.math.wisc.edu/~keisler/calc.html under a Creative Commons license. In addition, the chapter on differential equations (in the multivariable version) and the section on numerical integration are largely derived from the corresponding portions of Keisler’s book. 

Albert Schueller, Barry Balof, and Mike Wills have contributed additional material. This copy of the text was compiled from source at 7:57 on 12/16/2016. 

I will be glad to receive corrections and suggestions for improvement at guichard@whitman.edu.

Introduction

The emphasis in this course is on problems—doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems. The more problems you do the better you will be at doing them, as patterns will start to emerge in both the problems and in successful approaches to them. You will learn fastest and best if you devote some time to doing problems every day.

Typically the most difficult problems are story problems, since they require some effort before you can begin calculating. Here are some pointers for doing story problems:

1. Carefully read each problem twice before writing anything. 

2. Assign letters to quantities that are described only in words; draw a diagram if appropriate. 

3. Decide which letters are constants and which are variables. A letter stands for a constant if its value remains the same throughout the problem. 

4. Using mathematical notation, write down what you know and then write down what you want to find. 

5. Decide what category of problem it is (this might be obvious if the problem comes at the end of a particular chapter, but will not necessarily be so obvious if it comes on an exam covering several chapters). 

6. Double check each step as you go along; don’t wait until the end to check your work. 

7. Use common sense; if an answer is out of the range of practical possibilities, then check your work to see where you went wrong.   Download

Purpose of the GRE Subject Tests

The GRE Subject Tests are designed to help graduate school admission committees and fellowship sponsors assess the qualifications of applicants in specific fields of study. The tests also provide you with an assessment of your own qualifications.

Scores on the tests are intended to indicate knowledge of the subject matter emphasized in many undergraduate programs as preparation for graduate study. Because past achievement is usually a good indicator of future performance, the scores are helpful in predicting success in graduate study. Because the tests are standardized, the test scores permit comparison of students from different institutions with different undergraduate programs. For some Subject Tests, subscores are provided in addition to the total score; these subscores indicate the strengths and weaknesses of your preparation, and they may help you plan future studies.

The GRE Board recommends that scores on the Subject Tests be considered in conjunction with other relevant information about applicants. Because numerous factors influence success in graduate school, reliance on a single measure to predict success is not advisable. Other indicators of competence typically include undergraduate transcripts showing courses taken and grades earned, letters of recommendation, and GRE General Test scores. For information about the appropriate use of GRE scores, see the  Each new edition of a Subject Test is developed by a committee of examiners composed of professors in the subject who are on undergraduate and graduate faculties in different types of institutions and in different regions of the United States and Canada. In selecting members for each committee, the GRE Program seeks the advice of appropriate professional associations in the subject.

The content and scope of each test are specified and reviewed periodically by the committee of examiners. Test questions are written by committee members and by other university faculty members who are subject-matter specialists. All questions proposed for the test are reviewed and revised by the committee and subject-matter specialists at ETS. The tests are assembled in accordance with the content specifications developed by the committee to ensure adequate coverage of the various aspects of the field and, at the same time, to prevent overemphasis on any single topic. The entire test is then reviewed and approved by the committee.

Subject-matter and measurement specialists on the ETS staff assist the committee, providing information and advice about methods of test construction and helping to prepare the questions and assemble the test. In addition, each test question is reviewed to eliminate language, symbols, or content considered potentially offensive, inappropriate for major subgroups of the testtaking population, or likely to perpetuate any negative attitude that may be conveyed to these subgroups.

Because of the diversity of undergraduate curricula, it is not possible for a single test to cover all the material you may have studied. The examiners, therefore, select questions that test the basic knowledge and skills most important for successful graduate study in the particular field. The committee keeps the test up-to-date by regularly developing new editions and revising existing editions. In this way, the test content remains current. In addition, curriculum surveys are conducted periodically to ensure that the content of a test reflects what is currently being taught in the undergraduate curriculum. Download

Literacy and numeracy catch-up strategies

Introduction 

This paper examines catch-up strategies and interventions which are specifically aimed at pupils who are behind in literacy and numeracy. The paper looks at strategies used in both primary schools and secondary schools, as some interventions aimed at primary school pupils may be applicable and work with older pupils too (Singleton, 2009). It also includes some generic strategies which can be beneficial to low attainers. Finally, the paper looks at effective practice during transfer and transition from primary to secondary schools.

Definition of low attainment

Low attainment is defined as attainment below age-related expectations in a particular curriculum subject or skill. This includes basic skills such as literacy and numeracy, and higher order or conceptual skills.

Who are the low attainers?

There are groups of consistent low attainers across the Key Stages, including: boys, pupils eligible for Free School Meals (FSM), some ethnic minority groups, pupils with English as an Additional Language (EAL), pupils with Special Educational Needs (SEN), pupils with high rates of mobility between schools, and Looked After Children (LAC). These characteristics often interact and place a pupil at increased likelihood of underachievement. Low attainment is often due to complex interactions of a variety of social/demographic factors.

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