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How Old Is The Shepherd? – Robert Kaplinsky
- Article author: robertkaplinsky.com
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- Summary of article content: Articles about How Old Is The Shepherd? – Robert Kaplinsky P.S: The correct answer is clearly 23-27 years old, assuming he started shepherding at 16-18 and roughly doubled his flock every year. But how … …
- Most searched keywords: Whether you are looking for How Old Is The Shepherd? – Robert Kaplinsky P.S: The correct answer is clearly 23-27 years old, assuming he started shepherding at 16-18 and roughly doubled his flock every year. But how … How Old Is The Shepherd?, 32 eighth grade students answer the question “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”
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How Old Is The Shepherd? – Robert Kaplinsky
- Article author: mystudentvoices.com
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- Summary of article content: Articles about How Old Is The Shepherd? – Robert Kaplinsky There are 125 sheep and 5 dogs in a flock. How old is the shepherd? Got it yet? Of course you haven’t. There is no way to discern the age of … …
- Most searched keywords: Whether you are looking for How Old Is The Shepherd? – Robert Kaplinsky There are 125 sheep and 5 dogs in a flock. How old is the shepherd? Got it yet? Of course you haven’t. There is no way to discern the age of … How Old Is The Shepherd?, 32 eighth grade students answer the question “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”
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How old is the shepherd? – ProQuest
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- Summary of article content: Articles about How old is the shepherd? – ProQuest I think the shepherd is 25 years old. In this child’s world, mathematics is seen as a set of rules — a collection of procedures, actually — that must … …
- Most searched keywords: Whether you are looking for How old is the shepherd? – ProQuest I think the shepherd is 25 years old. In this child’s world, mathematics is seen as a set of rules — a collection of procedures, actually — that must … Explore millions of resources from scholarly journals, books, newspapers, videos and more, on the ProQuest Platform.
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How Old Is The Shepherd?
- Article author: riddlesbrainteasers.com
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How Old Is The Shepherd
how old is the shepherd
- Article author: capstone.extension.harvard.edu
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- Summary of article content: Articles about how old is the shepherd shepherd is 25 years old. In this child’s world, mathematics is seen as a set of rules a collection of procedures, actually that must first be. …
- Most searched keywords: Whether you are looking for how old is the shepherd shepherd is 25 years old. In this child’s world, mathematics is seen as a set of rules a collection of procedures, actually that must first be.
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There are 125 sheeps in a flock, and 5 sheepdogs. How old is the shepherd? – Quora
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- Summary of article content: Articles about There are 125 sheeps in a flock, and 5 sheepdogs. How old is the shepherd? – Quora There is no way to figure out the age of the shepherd from the size of his flock. It’s a trick question. …
- Most searched keywords: Whether you are looking for There are 125 sheeps in a flock, and 5 sheepdogs. How old is the shepherd? – Quora There is no way to figure out the age of the shepherd from the size of his flock. It’s a trick question. There is no way to figure out the age of the shepherd from the size of his flock. It’s a trick question.
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Making Sense of Word Problems – Google Sách
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- Summary of article content: Articles about Making Sense of Word Problems – Google Sách Updating …
- Most searched keywords: Whether you are looking for Making Sense of Word Problems – Google Sách Updating Word problems have been a staple of mathematics instruction for centuries, yet the rationale for their use has remained largely unexamined. A range of findings have shown how students consistently answer them in ways that fail to take account of the reality of the situations described. This monograph reports on studies carried out to investigate this “suspension of sense-making” in answering word problems.In Part One, a wide range of examples documenting the strength of the phenomenon is reviewed. Initial surprise at the findings was replaced by a conviction that the explanation lies in the culture of the mathematics classroom, specifically the rules implicitly governing the nature and interpretation of the word problem genre.This theoretical shift is reflected in Part Two. A detailed analysis of the way in which word problems are currently taught in typical mathematical classrooms is followed by reviews of design experiments illustrating how, by immersing students in a fundamentally changed learning environment, they can acquire what the authors consider to be more appropriate conceptions about, and strategies for doing, word problems.Part Three turns to a wider discussion of theoretical issues, a further analysis of the features of the educational system considered responsible for outcomes detrimental to many students’ understanding and conception of mathematics, and suggestions for rethinking the role of word problems within the curriculum.
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How Old is The Shepherd? Revisited in 3rd Grade | Under the Dome
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- Summary of article content: Articles about How Old is The Shepherd? Revisited in 3rd Grade | Under the Dome How Old is The Shepherd? Revisited in 3rd Grade · 3 out of 19 students made sense of the problem (15.8%) · One student added 125 five times. · One … …
- Most searched keywords: Whether you are looking for How Old is The Shepherd? Revisited in 3rd Grade | Under the Dome How Old is The Shepherd? Revisited in 3rd Grade · 3 out of 19 students made sense of the problem (15.8%) · One student added 125 five times. · One … Over the past few weeks, I’ve shown the How old is the shepherd? problem to both of my kids and then shown them the video from Robert Kaplinsky’s blog. Both were shocked at how many students don’t pay attention to what is happening in the problem. Connor even said, “I guess I’m not one of the 24.” Here is…
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Thoughts about Teaching
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How old is the shepherd?
Each weekday during the school year, some 25 million children study mathematics in U.S. schools under the careful supervision of classroom teachers, using textbooks that publishers have spent millions of dollars to develop and print. With this impressive investment of human and monetary capital, why is it that our students perform as if their curriculum and instruction were on the cutting edge of mediocrity? Why is it that, on virtually every international comparison of teaching and learning of mathematics, the performance of children in the U.S. ranks near the bottom?
In order to focus discussion, consider the following nonsensical problem:
There are 125 sheep and 5 dogs in a flock. How old is the shepherd?
Researchers report that three out of four schoolchildren will produce a numerical answer to this problem.(1) A transcript of a child solving this problem aloud reveals the kind of misinformed conception of mathematics that many children hold:
125 + 5 = 130 … this is too big, and 125 – 5 = 120 is still too big … while 125 / 5 = 25. That works! I think the shepherd is 25 years old.
In this child’s world, mathematics is seen as a set of rules — a collection of procedures, actually — that must first be memorized and then correctly applied to produce the answer. Examining the transcript, we see that this student is not without reasoning ability. Indeed, the accurate deduction about the appropriateness of the shepherd’s age shows some sense-making. In spite of this reasoning, however, the child apparently feels compelled to produce a numerical answer. How frequently teachers see this eagerness to begin writing and manipulating numbers before the situation is fully understood!
America has produced a generation of students who engage in problem solving without regard for common sense or…
How Old is The Shepherd? Revisited in 3rd Grade
Over the past few weeks, I’ve shown the How old is the shepherd? problem to both of my kids and then shown them the video from Robert Kaplinsky’s blog. Both were shocked at how many students don’t pay attention to what is happening in the problem. Connor even said, “I guess I’m not one of the 24.”
Here is my son, Connor, with his response to the problem:
Unfortunately, his first statement, “That’s stupid!” was not caught on video!
My daughter, Lura, with her response:
Last Saturday, after ambushing one of my daughter’s friends with the problem while she was visiting, Kim (my wife) became more curious about the problem, so I showed the video to her and shared some of the data on Kaplinsky’s blog. She was also shocked at the results. We had a brief conversation that went something like this:
Me: This is why we need to teach math content through patient problem solving and sense making!
Kim: Ok. (with a look that says, I know you’re passionate about this, and that it’s important. We’ll talk later. Go make a 3-act video and post it to your blog.)
Me: Ok.
It was left alone until this morning. It’s just me, but I like to think we would’ve talked sooner if I hadn’t been fighting a cold. She texted me and asked me to send her the Shepherd problem. I did, but only with the requirement that she share what she does with it.
Kim (and her co-teacher) gave the problem to each of their students and I just received the results:
3 out of 19 students made sense of the problem (15.8%)
One student added 125 five times.
One student reasoned that by the time you had 5 dogs and 125 sheep, you have to be in your fifties.
One student divided 125 by 5.
6 students added 125 and 5 to get 130.
3 computed an operation with the two numbers incorrectly
The other students guessed or showed no reasoning.
Now the good stuff:
One student (an autistic child) shared his reasoning about the problem with his classmates:
“The shepherd has no-o-o-othing (said as a sheep might say it) to do with the sheep and the dogs.”
Both teachers lost it!
Take aways from this:
It’s best that we start teaching math content through problem solving early and consistently K-12 and beyond.
Making sense of mathematics needs to be a priority for all students. (SMP 1)
All students bring something of value to a classroom.
Stories like the student who shared his reasoning sometimes get us through days that are not so much like this.
Below, you will find some of the students’ reasoning.
How old is the shepherd_
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