A ktm reader sends this question from her daughter's 2nd grade math book.
24 comments:
Anonymous
said...
As far as I can tell, the "mode" is the least-used of all descriptive statistics. Many data sets don't even have a mode although they will have a min, max, median, and mean. But mode is the easiest, of the the statistics with a special name, to define; thus is it taught pointlessly to 7th graders around the land. And now 2nd graders?
The mode is 4, the value you have the most of--the one that's most common. It's a good term to know. Occasionally, you'll hear a warning that some data set is "bimodal," like a Bactrian camel, and you'll be reminded to not assume that the "average" is "average."
You could sample ANY distribution and have that happen. In fact, you are almost guaranteed to have no mode if you sample a continuous distribution with enough precision. In continuous cases, you often group things into ranges (10-12, 12-14, 14-16, etc.) so you can get some repeat values.
What you are looking at is a stripped-down bar graph, in which each X in the column over a numeral represents the number of times that numeral occurs. The stack of X's over the 4 is tallest. Therefore, 4 is the most commonly occurring value, a.k.a., the mode.
Yes, Anonymous, it's the former. Each X is a data point. The stacks are bins into which you throw the data points for counting purposes, and the counts showing how many Xs are in each bin aren't data points themselves, just part of the analysis. If one of the bins ends up with a taller stack of data points than any other bin, that bin is the mode. The count of how many Xs end up in the mode bin isn't called anything that I know of. As long as it's the biggest its bin becomes the mode.
Thank you. That's what I thought, but the teacher said that the correct answer was 2. I spoke with her today again. She double checked the teacher's manual and the correct answer is 4.
I missed the point of this post entirely. That the mode was 4 was obvious. I thought it was being highlighted because they called the histogram a line graph, which it clearly is not.
According to most state standards. The image is of a line plot:
"A graphical display of a set of data where each separate piece of data is shown as a dot or mark above a number line." dpi.wi.gov/standards/mathglos.html
Mode is not not included in the CCSSM at 2nd grade, so what will happen to this textbook? Will the teacher be instructed to skip the lesson? Will the textbook be updated, then no one can afford the new books? Will they just keeping teaching mode because its in their materials? Just sayin'
This is interesting, because if this is considered a "line plot" that definition does not match current use. Or at least, my current use and I assume also that of anyone who programs much in Matlab at a minimum. A line plot is a plot of a line (or curve), while this is clearly a histogram.
kcab- This definition of Line Plot seems to be from the (elementary) education world. Google "line plot" +images -> most hits are from a math coaching or education sites. Google histogram, and the hits are, well, less from the ed world.
Line plots are identified in the Common Core State Standards for Mathematics in grades 2, 4 & 5: 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
5.MD2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
And the CCSSM Glossary defines a line plot as: Line plot. A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot. (Adapted from Wisconsin Department of Public Instruction, op. cit.)
Yes, I noticed, but I think that perhaps the ed world is making a mistake. Histogram is the accepted term for this type of graph. If schools are teaching terms like mode in the first place, they might as well get the name of the type of graph correct.
histogram - see Wikipedia
Line plot - this page in old Matlab documentation is an example of typical usage: http://www.mathworks.com/help/matlab/creating_plots/line-plots-of-matrix-data.html or, look at your chart types in Excel. (Excel doesn't use the term line plot, but does use line graph or line chart.)
Sigh, I just don't like things like this because they remind me of an awful early elementary teacher who told my daughter lies like 2-3 = 0.
"This is the scary part. She had to check the manual"
Unfortunately there is more. She also said that next year she will accept both answers (2 and 4) as valid because "kids get very confused with this concept".
I didn't even know how to respond to that but looking back I should have said that if a concept is too difficult for a second grader to grasp then it should be taught when he/she is older instead of teaching it wrong and accepting a wrong answer. So sad... :(
I hate the term "line plot", because I get it mixed up with "line graph". I can't figure out why a line plot is called a line plot, since there aren't any lines in it, but oh well. I prefer pictogram (just with very simple pictures), which, of course, is closely related to histogram (only with discrete values for the bins).
Coming in a little late here, but this is too timely and interesting for me to pass-up.
About two weeks ago I downloaded Ohio's 3rd grade math assessment test to give to my son as a check on how he's coming along at school. (BTW, we're not from Ohio, it just happened to be one of the top hits from my search term.) One of the questions was this very one. I was following along while he worked on it, and when I saw this question my first thought was what a ridiculous question. I couldn't remember mode myself! No one uses mode, except as mentioned already, in the use of bi-modal to make a distinction with normal or Gaussian, which unfortunately didn't occur to me at the time.
So, I used it as an opportunity to teach him test-taking skills. I said I have no idea what mode is either, but we can figure it out. All these tests have to have a single right answer in order for the computers to be able to grade them. We can figure out the right answer by ruling out all the answers that are not unique. Two is unique, because it is the smallest, but we already have a word for smallest: minimum. Of 3, 4, and 5, which one is unique? 4 is both because it has the most and because it is in the middle. So, 4 is the right answer.
Then I told him, incidentally, I do know the word for the middle number is median; so, that tells us mode must mean the number that has the most.
Finally, I told him the important thing about taking these tests is to never panic and make a wild guess. If you aren't sure, always look at the answers and try and pick the one that is unique. For good or for bad, test taking is an important skill in the 21st century.
24 comments:
As far as I can tell, the "mode" is the least-used of all descriptive statistics. Many data sets don't even have a mode although they will have a min, max, median, and mean. But mode is the easiest, of the the statistics with a special name, to define; thus is it taught pointlessly to 7th graders around the land. And now 2nd graders?
The mode is 4, the value you have the most of--the one that's most common. It's a good term to know. Occasionally, you'll hear a warning that some data set is "bimodal," like a Bactrian camel, and you'll be reminded to not assume that the "average" is "average."
Glen - you could sample a bi-modal distribution and end up with a set of data that has no mode. There might be no repeated values at all.
You could sample ANY distribution and have that happen. In fact, you are almost guaranteed to have no mode if you sample a continuous distribution with enough precision. In continuous cases, you often group things into ranges (10-12, 12-14, 14-16, etc.) so you can get some repeat values.
Is this 2,2,3,3,3,3,4,4,4,4,4,5,5,6 OR 2,4,5,2,1?
That's my question.
It is 2, 2, 3, 3, 3, etc.
What you are looking at is a stripped-down bar graph, in which each X in the column over a numeral represents the number of times that numeral occurs. The stack of X's over the 4 is tallest. Therefore, 4 is the most commonly occurring value, a.k.a., the mode.
Yes, Anonymous, it's the former. Each X is a data point. The stacks are bins into which you throw the data points for counting purposes, and the counts showing how many Xs are in each bin aren't data points themselves, just part of the analysis. If one of the bins ends up with a taller stack of data points than any other bin, that bin is the mode. The count of how many Xs end up in the mode bin isn't called anything that I know of. As long as it's the biggest its bin becomes the mode.
Thank you. That's what I thought, but the teacher said that the correct answer was 2. I spoke with her today again. She double checked the teacher's manual and the correct answer is 4.
I missed the point of this post entirely. That the mode was 4 was obvious. I thought it was being highlighted because they called the histogram a line graph, which it clearly is not.
"She double checked the teacher's manual and the correct answer is 4."
This is the scary part. She had to check the manual. Teaching mode means that they can say that they are teaching statistics.
What curriculum is this from?
According to most state standards. The image is of a line plot:
"A graphical display of a set of data where each separate piece of data is shown as a dot or mark above a number line."
dpi.wi.gov/standards/mathglos.html
Mode is not not included in the CCSSM at 2nd grade, so what will happen to this textbook? Will the teacher be instructed to skip the lesson? Will the textbook be updated, then no one can afford the new books? Will they just keeping teaching mode because its in their materials? Just sayin'
For your elementary student memorizing enjoyment, there is a card/poster put out by a company in Texas that uses the visual:
MMMode
The median graphic is :
meDIAn
She double checked the teacher's manual and the correct answer is 4.
Well at least that's something.
I was thinking the manual had it wrong, too!
I'm guessing you were typing meDIan, not meDIAn, and lingered a little too long on the shift key. But maybe what it should really be is adEImn. ;-)
(And that's funny--the captcha I now have to type is "nmedian 4". The machine gods are watching.)
This is interesting, because if this is considered a "line plot" that definition does not match current use. Or at least, my current use and I assume also that of anyone who programs much in Matlab at a minimum. A line plot is a plot of a line (or curve), while this is clearly a histogram.
"Glen said...
I'm guessing you were typing meDIan, not meDIAn"
meDIan is correct.
The curse of the ipad and fat fingers.
And you can find these math cards here: Lone Star Learning Math Vocab Cards
kcab- This definition of Line Plot seems to be from the (elementary) education world. Google "line plot" +images -> most hits are from a math coaching or education sites. Google histogram, and the hits are, well, less from the ed world.
Line plots are identified in the Common Core State Standards for Mathematics in grades 2, 4 & 5:
2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units
4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
5.MD2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
And the CCSSM Glossary defines a line plot as:
Line plot. A method of visually displaying a distribution of data values where
each data value is shown as a dot or mark above a number line. Also known as a dot plot. (Adapted from Wisconsin Department of Public Instruction, op. cit.)
Yes, I noticed, but I think that perhaps the ed world is making a mistake. Histogram is the accepted term for this type of graph. If schools are teaching terms like mode in the first place, they might as well get the name of the type of graph correct.
histogram - see Wikipedia
Line plot - this page in old Matlab documentation is an example of typical usage: http://www.mathworks.com/help/matlab/creating_plots/line-plots-of-matrix-data.html
or, look at your chart types in Excel. (Excel doesn't use the term line plot, but does use line graph or line chart.)
Sigh, I just don't like things like this because they remind me of an awful early elementary teacher who told my daughter lies like 2-3 = 0.
While we're at it, the word is datum.
"This is the scary part. She had to check the manual"
Unfortunately there is more. She also said that next year she will accept both answers (2 and 4) as valid because "kids get very confused with this concept".
I didn't even know how to respond to that but looking back I should have said that if a concept is too difficult for a second grader to grasp then it should be taught when he/she is older instead of teaching it wrong and accepting a wrong answer. So sad... :(
If a concept is too difficult for a teacher to grasp, she shouldn't be teaching that subject.
The book looks bad enough, but if the teacher doesn't even understand the math so poorly expressed, it's downhill from there.
I hate the term "line plot", because I get it mixed up with "line graph". I can't figure out why a line plot is called a line plot, since there aren't any lines in it, but oh well. I prefer pictogram (just with very simple pictures), which, of course, is closely related to histogram (only with discrete values for the bins).
Coming in a little late here, but this is too timely and interesting for me to pass-up.
About two weeks ago I downloaded Ohio's 3rd grade math assessment test to give to my son as a check on how he's coming along at school. (BTW, we're not from Ohio, it just happened to be one of the top hits from my search term.) One of the questions was this very one. I was following along while he worked on it, and when I saw this question my first thought was what a ridiculous question. I couldn't remember mode myself! No one uses mode, except as mentioned already, in the use of bi-modal to make a distinction with normal or Gaussian, which unfortunately didn't occur to me at the time.
So, I used it as an opportunity to teach him test-taking skills. I said I have no idea what mode is either, but we can figure it out. All these tests have to have a single right answer in order for the computers to be able to grade them. We can figure out the right answer by ruling out all the answers that are not unique. Two is unique, because it is the smallest, but we already have a word for smallest: minimum. Of 3, 4, and 5, which one is unique? 4 is both because it has the most and because it is in the middle. So, 4 is the right answer.
Then I told him, incidentally, I do know the word for the middle number is median; so, that tells us mode must mean the number that has the most.
Finally, I told him the important thing about taking these tests is to never panic and make a wild guess. If you aren't sure, always look at the answers and try and pick the one that is unique. For good or for bad, test taking is an important skill in the 21st century.
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