Article Review: Helpful

The Dating Game

The main purpose of this paper is, paraphrasing the author, "to cultivate a tendency in students to search for and recognize special properties of small natural numbers by looking for mathematical relationships in the dates in a year." The article does this and more by investigating relationships involving special numbers, such as pi.

There are four very important strengths to this paper.

• The relationships will be interesting, like puzzles, to most readers of Mathematics Teacher.
  
  
• The relationships result in challenging and engaging activities for students whose teachers use them.
  
  
• This article includes activities appropriate for all secondary mathematics classes.
  
  
• The use of these activities will help develop students' number sense.

But there are also some correctable problems with this paper. I will list them here and give examples under the specific points listed later in this review.

• Since the paper goes beyond properties of natural numbers to special numbers, the author should rewrite the introduction to express the broader goals that the paper accomplishes.
  
  
• Answers should be given to all of the problems.
  
  
• The author assumes the reader is familiar with all of the concepts discussed, which may not be the case. For this reason, I had some difficulty reading certain parts [see comments 1) and 4)] of this paper. The author therefore needs to carefully define terms used, and give a brief introduction to some topics.
  
  
• There needs to be a concluding part that ties the other parts of the paper together, making it clear how this paper connects to the classroom.

For these reasons, I suggest publishing an appropriately revised version of this manuscript, possibly in Sharing Teaching Ideas.

I now give some specific points that need to be addressed.

1) The first paragraph under "Constants": Most teachers will understand why March 14 goes with pi, but may not know what October 24 and February 10 have to do with 1K (I don't). I do not know what number phi represents, nor why it is related to June 18 and to August 13. A little explanation is in order.

(On another note, July 22 goes better with pi if using European dating in which the day is given before the month. The same is true for July 19 and e. In particular, the notation 22/7 and 19/7 is more suggestive of the relationship. It seems appropriate to talk about relationships in both American and European notation.)

2) Under "Primes," the author might define the term "concatenation."

3) Under "Christmas," not all Mathematics Teacher readers and their students are Christians. It would be good if there were relationships for important dates of other religions. It would help to have answers to all questions, such as the last question in this section.

4) Under "Including the Day of the Year," it would be clearer if there also was an example for the M, DM, and DY cases. For example, 2/17/48 means that February 17 is the 48th day of the year.

In the second paragraph of this section, it would be helpful to note what is meant by "most Fibonacci" of dates. It might help to explain what a Fibonacci number is. I assume "most Fibonacci" means that M, DM, and DY are all Fibonacci numbers. The author might just exclude January dates instead of defining them as trivial.

In the third paragraph, this famous mathematician should be identified.

5) The digital clock idea seemed to stray from the main point of this paper. While this was also interesting, it should be omitted.

As for overall comments, it would be helpful to give more details about how the author actually uses these questions in the classroom (along with actual student reactions). It would also be good to reorganize this paper in a way that ties the different sections together.

(End of Review)

Analysis of Review: Helpful

The beginning summarizes what the reviewer believes is the intent and content of the article. This is followed by the reviewer's opinion about the specific strengths of the paper. The strengths relate to what readers of the Mathematics Teacher will get out of this paper.

The reviewer helped the author focus on broader goals for the paper without suggesting alternative goals beyond or in place of the author's intentions. For example, in the first paragraph, the reviewer stated "The article does this and more by investigating relationships involving special numbers, such as pi." In the second paragraph, "since the paper goes beyond properties of natural numbers to special numbers, the author should rewrite the introduction to express the broader goals that the paper accomplishes." In the last paragraph of the review, "it would be helpful to give more details about how the author actually uses these questions in the classroom."

Next come weaknesses of the paper. Some of the weaknesses relate to difficulties that typical readers will have in reading this paper, such as not defining terms, not giving answers, and not giving an overall summary. The reviewer did not go into specifics about grammar and syntax, which will be taken care of during the editing process if the manuscript is accepted.

The reviewer noted specific places in the paper where he or she had difficulty following the paper. If the reviewer is having difficulty, others also will have difficulty.

The reviewer noted where the author missed the diversity of many classrooms (referring to Christmas).