Mathematics and Modern-Day Mathematics

Mathematics and Modern-Day Mathematics

Instructions/Descriptions

Research a known historical mathematician (Examples: Euler, Newton, Leibniz, Galois, Lorentz)

Discover the mathematician contributions to modern-day mathematics

Explain how this mathematics may have influenced modern-day life or how it has caused historical events in the world

Discover the importance of mathematics

Science Social Psychology on Self-Incriminating Confessions

[Adapted from: Kosslyn, S.M. & Rosenberg, R.S. (2001).Psychology: The Brain, The Person, The World. Boston: Allyn & Bacon.]

The QAMRI method provides a means for critically evaluating experiments.It helps you to find connections between theory and data by making explicit the question being asked, the approach used to answer it, and the implications of the answer.This must be done in your own words, not the words used by the author(s) of the journal article.

If multiple experiments are reported in the paper, do each step for the set of experiments together, rather than separately for each experiment.

Bullet points are fine, and a brief summary is expected (within 2 pages, double-spaced). This means you need to be concise and capture the big ideas, not the details.

Also feel free to note anything about the article that you do not understand.

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Use the headings below in your QAMRI article summary.

Put a title block at the top of the page, consisting of

Your name

The full citation of the article (in APA format).

Q stands for Question

All research begins with a question, and the point of the research is to answer it.For example, we can ask whether a placebo is better than no action in alleviating depression.For most journal articles, the General Introduction should tell the reader what question the article is addressing, and why it is important enough that anyone should care about the answer.

Questions fall into two categories: broad and specific. In your QAMRI, state both the broad and the specific questions being asked.Broad questions are typically too general to answer in a single experiment, although one should view the experiment as one step on a journey to answer the broad question.An example of a broad question might be “Does language influence perception?”This sort of question provides the general topic of the paper and can only be answered through compiling many experimental results. In contrast, the specific question can typically be addressed in a single experiment or set of experiments. A specific question might be “If one language has a specific term for one color, and another language does not have any term for that color, will speakers of the two languages perceive the color differently?” Again, be sure to identify the broad and specific question.

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A stands for Alternatives

Good experiments consider at least 2 possible alternative answers to a specific question and explains why both answers are plausible.For example, the possibility that speakers of different languages will perceive colors differently is plausible based on evidence that top-down processes can affect perception.The alternative hypothesis, that language does not influence perception of color, is also plausible because color perception in particular might be impervious to top-down influences.That is, it might be based solely on properties of the visual system which are unaffected by language.When describing an existing article or when proposing an experiment, you should identify the alternatives the authors considered.There are always at least 2 alternatives: that factor X will show an effect, or that it won’t (that a null result will be obtained).If possible, identify other alternative patterns as well.

M stands for Method

This section identifies the procedures that were used to implement research design.It should state the independent variable (the factor being experimentally manipulated or observed) and the dependent variable (the behavior being measured at the outcome) of the experiment.It should also describe the participants, including whether and how participants were divided into groups receiving different experimental manipulations.Briefly describe the experimental procedure.

R stands for Results

In your own words, what was the outcome of the experiment?Describe the results of the primary measures of interest.For example, did different subject groups yield different group means? Or did the entire subject population produce a distinctive pattern of responses?Describe that pattern in a straightforward way. You do not need to include results that do not address the primary research question.

I stands for Inferences

What can the results of the experiment tell us about the alternatives?If the study was well designed, the results should allow you to eliminate at least one of the possible alternatives.For example, if a language has a relevant color word but the speakers of that language respond to the color no differently than speakers of a language lacking a term for the color, then the experiment supports the view that language does not influence color perception.

At this point, take a step back and think about any potential problems with the experiment that could have led to the pattern of results obtained.Were there confounds that could have caused the results?For example, if they did find a difference between the subject groups, are there other ways in which the groups differ that are not language-related?Might this have caused the result?In addition, this is the section in which to consider the hypothetical next step in answering the broad question. If you were to conduct a follow-up experiment, what would it be (hint: think of questions that remain unanswered by the present results, and sketch a study that could bear on one or more of those questions)?

Mathematics and Modern-Day Mathematics

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