*Mathematics & Statistics: Lab Reports for Math

   Though it may be new to you, lab reports do exist in Mathematics and it is expected that each student be able to elegantly compose their thoughts for each given lab. The point of each lab assignment is to engage the student actively in the material so as to provide a "bigger picture" behind theorems, results and/or processes. Each lab also helps the student recognize specific strengths/weaknesses. 

Writing a report for mathematics can be a chore, especially if you aren't sure where to begin. Math isn't a subject that you usually write about so if you are asked to write a math report, you might need some help. Some math reports that you might need to do include describing a quadratic equation, writing about various ways to solve algebra questions, or writing about a specific discovery in the history of mathematics, such as negative numbers or imaginary numbers.

1. Discuss and Determine the Problem

   • Discuss with your teacher, classmates or parents what the math problem or math issue might be that you are writing about. This will enable you to get started on your report. Make a list of the various subjects or you might write a paragraph about what you are writing about. The problem that you come up with could be anything from "How to Solve a Multiplication Problem" to "Strategies for Teaching Math To Students." You will need to narrow your problem to one concrete sentence or idea, so that you can write a report about it.

   Research Steps and Processes

   • Research online or in mathematics books in the library the steps and processes that are going to be needed to solve the problem you have determined is at the root of your report. You might be able to use your own math book. Your teacher might have other suggestions for your research, such a talking to someone with a degree in math, or reading printed materials. Do the math required or figure out how to do the process you have to describe. This might mean you read books about the subject, practice the steps, or do experiments to come up with the best solution to the math problems.

   Write Out Steps

   • Write out the steps in your report as you would write any other report, using complete sentences and words. Don't use abbreviations and use the same number rules you use when writing for another class. For example, write out numbers from one to nine and use figures for numbers above 10. Write the steps in paragraph form, and only use bullet points if you have a list that you need to discuss within the report. Be sure that you have a conclusion at the end of your report in which you tie together all of the aspects you have talked about. Relate it to your beginning question.

What lab reports and scientific papers do:

•  
  • Persuade others
    to accept or reject hypotheses by presenting data and interpretations
  • Detail data, procedures, and outcomes
    for future researchers
  • Become part of the accepted body of scientific knowledge
    when published unless later disproved
  • Provide an archival record
    for reference and document a current situation for future comparison

Format:

The typical lab report includes: title, abstract, introduction, materials and methods, results, discussion, references and literature cited

Title

•  
  • Reflect the factual content with less than ten words in a straightforward manner
  • Use keywords researchers and search engines on the Internet will recognize

Abstract:

Summarize in a concise paragraph the purpose of the report,
data presented, and major conclusions in about 100 - 200 words.

Introduction:

•  
  • Define the subject of the report: "Why was this study performed?"
  • Provide background information and relevant studies: "What knowledge already exists about this subject?"
  • Outline scientific purpose(s) and/or objective(s): "What are the specific hypotheses and the experimental design for investigation?"

Materials and methods:

•  
  • List materials used, how were they used, and where and when was the work done (especially important in field studies)
  • Describe special pieces of equipment and the general theory of the analyses or assays used
  • Provide enough detail for the reader to understand the experiment without overwhelming him/her. When procedures from a lab book or another report are followed exactly, simply cite the work and note that details can be found there.

Results

•  
  • Concentrate on general trends and differences and not on trivial details.
  • Summarize the data from the experiments without discussing their implications
  • Organize data into tables, figures, graphs, photographs, etc. Data in a table should not be duplicated in a graph or figure
  • Title all figures and tables; include a legend explaining symbols, abbreviations, or special methods
  • Number figures and tables separately
    and refer to them in the text by their number, i.e.
    1. Figure 1 shows that the activity....
    2. The activity decreases after five minutes (fig. 1)

Discussion

•  
  • Interpret the data; do not restate the results
  • Relate results to existing theory and knowledge
  • Explain the logic that allows you to accept or reject your original hypotheses
  • Speculate as necessary but identify it as such
  • Include suggestions for improving your techniques or design, or clarify areas of doubt for further research

References & literature cited

•  
  • Cite only references in your paper and not a general bibliography on the topic
  • Alphabetize by last name of the author
  • Follow the recommended format for citations

General style

•  
  • Strive for logic and precision and avoid ambiguity, especially with pronouns and sequences
  • Keep your writing impersonal; avoid the use of the first person (i.e. I or we)
  • Use the past tense and be consistent within the report
    note: "data" is plural and "datum" is singular; species is singular and plural
  • Italicize all scientific names (genus and species)
  • Use the metric system of measurement and abbreviate measurements without periods (i.e. cm kg) spell out all numbers beginning sentences or less than 10 (i.e. "two explanations of six factors").
  • Write numbers as numerals when greater than ten (i.e. 156) or associated with measurements (i.e. 6 mm or 2 g)
  • Have a neutral person review and critique your report before submission