This month's tip comes to us from Joy Cooke, our instructor in the Teaching Math Fundamentals on the Way to Algebraic Thinking in Elementary School:

"The questions or prompts that we pose to students in mathematics lessons - and the way in which we respond to the answers to those questions - has a powerful impact on students' dispositions toward math, their thinking about math, and the development of their understanding.

Just as we want students to understand and make sense of what they read, we want them to make sense of the mathematics they are doing. This can't happen if teaching mathematics is limited to telling students how to follow procedures. Understanding is deepened when we consistently ask questions that communicate the expectation that students will use reasoning and explain their thinking. Such questions also give us a window into how our students are understanding what we are asking them to do.

• What is a possible answer to this problem? Who has a different possible answer?
• Tell me how you thought about that.
• What might be another way to do/think about that?
• How might you explain/prove that to someone else?
• Tell me how/why you think that is true.
• Why do you think that is so?
• Show me how you did that.
• Do you think that always happens?
• What do you think would happen if...?
• Can you draw a picture/show with models how that works?
• Do you see any patterns?

Often a student response to being asked to justify thinking is to assume that they must be wrong. Questions such as these, posed in response to all manner of answers and ideas, send the message that mathematics is about more than a right or a wrong answer, and helps to develop a thinking community where students engage in making sense of mathematics."

Finding funding for professional development initiatives can be an intimidating and time-consuming experience. It is difficult to find time to fill out the forms, compile the information, and research the diverse opportunities. We've highlighted grant opportunities in the past, but we thought that this month we could summarize some tips and resources to improve your chances of gaining one.

How to Begin

• When developing your idea, walk the line between innovative and realistic - think of imaginative projects that you can see working in real-life.
• Surf the web, consult with colleagues, visit the library, take note of projects you admire and where they gained their funding.
• Think local, look local. Many organizations in your area want to support education initiatives in their neighborhoods. Don't discard smaller grants, since they can supplement funds from other areas.
• As with an exam question, it is important to read the guidelines and instructions carefully.
• It is a discouraging step, but you must adapt the style, length, and tone of your application to meet the requirements of each funding body.
• Apply to a variety of funding bodies, but again, pay attention to different guidelines, expectations, and goals of an organization.
• Pick up the phone and call the program officer. Have an outline in front of you and some detailed questions. Take their advice into consideration but don't be limited by it.

Developing the Proposal

• Do your research - solicit support from an expert advisory committee and find reputable research sources that support your idea and the results you hope to achieve.
• Involve your colleagues and develop a team. Seek help from all levels - students, teachers, administrators, and outside experts. Ask for feedback as you plan. Include on your team a good researcher, a good proofreader, and a good networker.
• Develop an evaluation plan - how are you going to measure progress? Measure results? Measure efficacy? How much time will you devote to evaluation? Is this realistic?
• Develop a detailed budget. This is very important. Include relevant costs and not extraneous expenses.
• Find ways to supplement with other sources of funding in your school, district, or community. It impresses funding bodies if you have thought of other ways to fund your proposal.

Writing the Proposal

• Keep your language simple and straightforward. Think of newspaper writing, and how it communicates relevant information quickly.
• Be consistent - sections should follow on from each other. For example:
  Needs -> goals/objectives -> relevant steps to achieve goals -> evaluation that measures efficacy of these steps -> budget that includes costs for these steps.
• Break up long paragraphs of text with relevant lists, tables, statistics, and graphs.
• Match headlines in the grant-giver's guidelines to headlines in your application to make it easy for reviewers to find sections.
• Don't go overboard on attachments and supporting documents. If you are including supporting letters, make sure they are specific to the grant you're applying for and show in real terms how the supporters are going to contribute to the project (money, time, etc.).
• Use a fair amount of white space and a 12-point font, use bold font for effect only, and check margin requirements.
• Proofread
• Bring in outsiders and ask them to sum up the proposal when they've finished reading it. If they're confused on certain points, go back to the draft and clarify these areas.
• Follow submission procedures and deadlines to avoid falling at the last hurdle.

If you don't succeed...

• Ask for comments from the reviewers, even if you fail. Their thoughts will help you when constructing future grant applications.
• Write, in pen and on good paper, thank you notes to the reviewers.
• Don't be discouraged! Many great proposals are rejected each year.

If you do succeed...

• Keep your funding body informed of your progress on a regular basis (work this into your evaluation plan). Keep your school and students up-to-date on how things are going. Ask for continuous feedback.
• Note the problems you run into and the strategies and steps that work for use in future grant-funded projects.

Some of these ideas have come from a helpful article by: Joan Straumanis, former FIPSE (Fund for the Improvement of Post Secondary Education) Program Officer. It appears in Publish & Flourish: Become a Prolific Scholar, by Tara Gray. Published by Teaching Academy, New Mexico State University. Copyright © 2005 by Tara Gray. ISBN 0-9769302-0-X. Printed in the United States by Phillips Brothers Printers, Springfield, Illinois.

• Standards and accountability
• Efforts to improve teacher quality
• School climate
• Resource equity

A number of factors were judged in each category. For example, in Efforts to improve teacher quality, topics included: "Teacher education and qualifications", "Teacher assessment", "Professional support and training", and "Accountability for teacher quality." The average grade for states in this category was C+.

Generally speaking, C+ indicates a "need for improvement," but not "failure." Thus, in addition to the report, EdWeek featured a flurry of educational commentaries, case studies, and suggestions for improvement. New schools, national standards, and higher expectations are proposed.

A few of the commentators note that "grading" schools on their performance is, like grading students, somewhat artificial. As an article in the Harvard Education Letter on Grade Inflation points out, grades are only one way of measuring progress. In many cases a grade is used to indicate effort and induce motivation, instead of recording actual mastery of content.

With this in mind, how seriously should the results of the "Quality Counts" survey be taken? It is not an idle question, since the performance of public education systems is an international issue. Governments are concerned about "falling behind." The threat of the 21st century is held over the heads of our children - they won't be prepared, they won't be flexible, they won't be smart.

The threat of failure can motivate improvement, but in today's climate there appears to be a glut of negative feedback for educators that is unconstructive. Where are the articles about teachers and their students overcoming the challenges of crowded classrooms, the pressures of test-driven performance, and the lack of school resources? Where are the reports that give us practical, tested, and implementable steps to improve the schools that are falling behind?

When it comes to grading schools, it would pay for us to heed the advice of our own experienced teachers. They suggest that grades are not enough, that they require additional space to record how their students have progressed and to describe their relative strengths and weaknesses. Some argue qualitative assessments, done over time, can better demonstrate a student's achievement of goals, motivation and work habits, and next steps in learning.

Of course, realistically it takes time and effort to apply this concept, to a student or a school district. Grades are quicker to assign, easier to compare, and look better on a graph. But why not follow the example of a school like the Boston Arts Academy, quoted in the aforementioned article? They use both types of assessment for students: they give a grade to indicate general achievement and combine it with a narrative on all other aspects of performance. A biannual report that gives this kind of information about schools would be infinitely more enlightening than unaccompanied annual data on test scores.

As we continue to assess and evaluate our schools, in Australia, China, Egypt, or New York, let us also not forget that education will always be a work in progress. Schools that are working hard to overcome difficulties, incite learning, and engage their students deserve much more than a red letter - they deserve our respect.

Elinor Teele, WIDE World Editor

Do you have a strong opinion on a current educational issue? Would you like to write an opinion piece for our newsletter? Email wideeditor@gse.harvard.edu and propose a topic.

Newcomers and alums who visit the WIDE World website next month may be surprised to find that the landscape has suddenly changed. In the past fall we've been working on synthesizing our course structures, clarifying our offerings, and finding ways to display the hard work that goes on in classrooms and in our office itself.

Part of that process included a website renovation, and what you will see are some new ideas and more in-depth information about our professional development offerings.

We'd like to hear your feedback. Please explore the site and tell us what you think of the layout and the information presented.

We'd also like to hear your suggestions for further ways to expand the site and our offerings in the longer term. As those who have taken our courses know, we are very proud of our alumni and like to keep in touch with your achievements and progress. Please feel free to brainstorm with us on how we can reach more educators in the future.

February 17-19, 2006

WIDE World will be manning a booth and Dr. Lois Hetland, our former Focus on Student Understanding: Teaching for Understanding 1 course instructor, will be giving a talk at the AAIE (Association for the Advancement of International Education) Annual Conference in Boston, on February 18, 2006. Her talk is entitled: "International Educators and Online Courses: Sparking Connections."

March 22-24, 2006

WIDE World will be exhibiting at the Florida Educational Technology Conference in Orlando, FL. We're at Booth 569 - please come and ask us questions.

Have a classroom tip that utilizes Teaching for Understanding or a story to tell? Email wideeditor@gse.harvard.edu and tell us all about it.