Reminding them of the criteria. "This is a word problem and one of the criteria is correct interpretation of numbers in context." This is the best type of assistance.
"Keep thinking" questions and comments such as those mentioned elsewhere in this thread
Descriptive praise [EDIT: I realize I gave this short thrift originally. I should have said that among pedagogical techniques that are easy to implement, descriptive praise is IMHO the most powerful. Other suggestions in this post are much harder.]
Hints that reference success but require deep thinking to utilize. "I see you're stuck on exercise 38, but you aced last week's problem set and its last problem is quite relevant here."
Highlighting specific progress and excellence in front of the class and celebrating it. Even as little as a short applause or a cheer or giving them a token prize. "Last week, Joe was unhappy with his proof by induction. This week his induction proof got an A- and the grand prize of a $0.25 chocolate bar. Look at both proofs and tell me what improvements he made. Reference the criteria we discussed earlier."
Reminding them of the criteria. "This is a word problem and one of the criteria is correct interpretation of numbers in context." This is the best type of assistance.
"Keep thinking" questions and comments such as those mentioned elsewhere in this thread
Hints that reference success but require deep thinking to utilize. "I see you're stuck on exercise 38, but you aced last week's problem set and its last problem is quite relevant here."
Highlighting specific progress and excellence in front of the class and celebrating it. Even as little as a short applause or a cheer or giving them a token prize. "Last week, Joe was unhappy with his proof by induction. This week his induction proof got an A- and the grand prize of a $0.25 chocolate bar. Look at both proofs and tell me what improvements he made. Reference the criteria we discussed earlier."
Reminding them of the criteria. "This is a word problem and one of the criteria is correct interpretation of numbers in context." This is the best type of assistance.
"Keep thinking" questions and comments such as those mentioned elsewhere in this thread
Descriptive praise [EDIT: I realize I gave this short thrift originally. I should have said that among pedagogical techniques that are easy to implement, descriptive praise is IMHO the most powerful. Other suggestions in this post are much harder.]
Hints that reference success but require deep thinking to utilize. "I see you're stuck on exercise 38, but you aced last week's problem set and its last problem is quite relevant here."
Highlighting specific progress and excellence in front of the class and celebrating it. Even as little as a short applause or a cheer or giving them a token prize. "Last week, Joe was unhappy with his proof by induction. This week his induction proof got an A- and the grand prize of a $0.25 chocolate bar. Look at both proofs and tell me what improvements he made. Reference the criteria we discussed earlier."
EDIT: OP said that many students received good grades for the presentations and may have inferred that effort was not necessary. Overall, the comments and grading strike me as sending an inconsistent message.
More importantly, though, this quote is all about the teacher doing a lot of mathematical thinking while the students - presenters and audience - doing very little.
More importantly, though, this quote is all about the teacher doing a lot of mathematical thinking while the students - presenters and audience - doing very little.
EDIT: OP said that many students received good grades for the presentations and may have inferred that effort was not necessary. Overall, the comments and grading strike me as sending an inconsistent message.
More importantly, though, this quote is all about the teacher doing a lot of mathematical thinking while the students - presenters and audience - doing very little.
As students become more proficient in assessing their own work, you can start calling on them to present in front of the class. "Who has thoughts on this they'd like to share?" Or, more privately, you can speak to one student and say "Hey, listen, your work here is really elegant even though it's not quite complete. I know you don't like performing, but can I share a screenshot of that with the class?" After this, have the class discuss in terms of the pre-established criteria what makes these such shining examples. When they're done commenting, as the teacher, say "I'd give this a B+. Not bad for 5 minutes work! Here's a similar problem. Now, everyone, gimme some A+ quality work!"
Have students write in PENCIL a practice midterm as if it were the real thing, but do NOT count it for grades. Then, have them mark their own practice midterm in BRIGHT RED PEN, you guessed it, according to the criteria. (They might need a solution key, too.) Then, still in RED, each student writes a letter grade at the top of their test along with a bunch of specific comments to themselves on how to improve for the real midterm. Another student then approves the grade and comments, then submits everything to you and you give them written feedback on the whole thing, - but mainly the RED stuff - ideally at least a few days before the real midterm. Trust me - they will respond productively to this feedback!
As students become more proficient in assessing their own work, you can start calling on them to present in front of the class. "Who has thoughts on this they'd like to share?" Or, more privately, you can speak to one student and say "Hey, listen, your work here is really elegant even though it's not quite complete. I know you don't like performing, but can I share a screenshot of that with the class?" After this, have the class discuss in terms of the pre-established criteria what makes these such shining examples. When they're done commenting, as the teacher, say "I'd give this a B+. Not bad for 5 minutes work! Here's a similar problem. Now, everyone, gimme some A+ quality work!"
Have students write in PENCIL a practice midterm as if it were the real thing, but do NOT count it for grades. Then, have them mark their own practice midterm in BRIGHT RED PEN, you guessed it, according to the criteria. (They might need a solution key, too.) Then, still in RED, each student writes a letter grade at the top of their test along with a bunch of specific comments to themselves on how to improve for the real midterm. Another student then approves the grade and comments, then submits everything to you and you give them written feedback on the whole thing, ideally at least a few days before the real midterm. Trust me - they will respond productively to this feedback!
As students become more proficient in assessing their own work, you can start calling on them to present in front of the class. "Who has thoughts on this they'd like to share?" Or, more privately, you can speak to one student and say "Hey, listen, your work here is really elegant even though it's not quite complete. I know you don't like performing, but can I share a screenshot of that with the class?" After this, have the class discuss in terms of the pre-established criteria what makes these such shining examples. When they're done commenting, as the teacher, say "I'd give this a B+. Not bad for 5 minutes work! Here's a similar problem. Now, everyone, gimme some A+ quality work!"
Have students write in PENCIL a practice midterm as if it were the real thing, but do NOT count it for grades. Then, have them mark their own practice midterm in BRIGHT RED PEN, you guessed it, according to the criteria. (They might need a solution key, too.) Then, still in RED, each student writes a letter grade at the top of their test along with a bunch of specific comments to themselves on how to improve for the real midterm. Another student then approves the grade and comments, then submits everything to you and you give them written feedback on the whole thing - but mainly the RED stuff - ideally at least a few days before the real midterm. Trust me - they will respond productively to this feedback!