Math: Pen vs Pencil

Many math students are given strict instructions by their teachers to do all their work in pencil. I disagree.

The advantage of doing work in pencil is that:

  • it is easier to erase, so students are less likely to be paralyzed by “I am not sure this is correct, so I don’t dare write it down”

The disadvantages of working in pencil are that: Continue reading Math: Pen vs Pencil

What A Parent Wants From A School

As a parent, I look for two categories of attributes when choosing a school for my child:
– Ones which benefit my child directly
– Ones which benefit my child indirectly, by helping others (teachers, parents) do their jobs more effectively

Schools that satisfy more of the attributes in both categories are likely to have happier parents and more successful students.

The Administration and Teachers Should Help My Child

Directly By:

  • Being aware of history. Before the start of each school year, my child’s current teacher(s) should have reviewed all of
    – last years’ teacher comments for my child
    – my child’s transcript (all courses, all years at the school)
  • Helping my child to both pursue existing  Continue reading What A Parent Wants From A School

Short Assessment Grading: Add or Average?

Long assessments can waste precious class time unless there is much material to be assessed, but shorter assessments (with few questions) can cause small errors to have too big an impact on a student’s grade.

For example, consider the following assessment lengths where each question is worth 4 points, and the student has a total of two points subtracted from their score for errors:

# Questions Points % % Grade
1 2 / 4 50% F / F
2 6 / 8 75% D / C
3 10 / 12 83% C+/ B
4 14 / 16 88% B / B+
5 18 / 20 90% B+/ A-

The “% Grade” in the table above reflects a 7-point / 10-point per letter grade approach. A one question quiz is risky for students: they could get a failing grade for losing two points on the only question. Two question quizzes are only slightly less risky.  Only with three or more questions does this scenario start to minimize the risk of actively discouraging a student who loses several points.

Should quizzes therefore only have three or more questions? What if I don’t want the class to spend that much time on an assessment, or don’t have Continue reading Short Assessment Grading: Add or Average?

Unintended Consequences of a 0 – 100 Grading System

If a student makes four errors in the course of answering ten questions, what is an appropriate grade? Presumably, it would depend on the severity of the errors and the nature of the questions. Consider how your approach to grading might vary if students had been asked to:

– match ten vocabulary words to a word bank, or
– define each of ten words, then use each appropriately in a sentence

– complete ten 2-digit multiplication problems, or
– solve ten multi-step algebra problems, each requiring a unique sequence of steps

– answer ten questions similar to what they have seen for homework or in class, or
– answer ten questions unlike ones they have been asked before

Would you label each answer as right or wrong, then use percentage right as the grade?
Would you assign a number of points to each answer (if so, out of how many points per question)?
Would you assign a letter grade to each answer (whole letters only, or with +/-)?
What would you consider a “D” set of answers?
What would you consider an “A” set of answers?

Would your answers vary depending on whether you had created the assessment yourself, or were using someone else’s questions?

Many math/science teachers seem to use a percentage approach (based on total points earned or number correct) more often than any other, particularly when their school defines its letter grades using a 0 – 100 scale. Teachers of other subjects also use this scale often, but less so for “free-response” questions. While a percentage approach can work well for some assessments, it can have unintended consequences for others.

Similar Right/Wrong Questions

When asking a series of similar questions, such as Continue reading Unintended Consequences of a 0 – 100 Grading System

Flipped Classroom: It’s About Timely Formative Feedback

The phrase “Flipped Classroom” is appearing with increasing frequency in publications and blog postings. Yet, it seems to mean different things to different people. Many of the references I see to flipped classrooms are made by people or organizations who have a vested interest in selling goods or services, which probably affects their view of the issues.

As proposed by Salman Khan in his TED Lecture, flipping the classroom involves using internet-based video to move “lecture” out of the classroom to some other place and time of a student’s choosing. Class time can then be used for student problem solving and group work. Dan Meyer and others have critiqued aspects of Salman Khan’s approach, with some such as Michael Pershan offering constructive ideas for improvements.

Eric Mazur, a physics professor at Harvard, has also been advocating a “flipped” approach  – and for considerably longer than Salman Khan. His conception of “flipping” focuses on getting students to Continue reading Flipped Classroom: It’s About Timely Formative Feedback

Grant Wiggins on Mathematics Education

Grant Wiggins was the keynote speaker last night at the annual “Anja S. Greer Conference on Mathematics, Science and Technology” hosted by Phillips Exeter Academy in Exeter, NH. The focus of his talk was mathematics education, and the points that were noteworthy to me included the following:

Increasingly, schools and standards bodies are setting their goal for mathematics education to be the development of good problem solvers. Yet,
– few schools focus their curriculum on problem solving
– nationally, dismal percentages of students can successfully solve problems of types they have been taught to solve, let alone problems they are not familiar with
– a significant percentage of students hate their mathematics courses

We face some big questions that are challenging to answer:
– What is the problem with mathematics education today?
– What are we going to do to address it?
This is the problem that math teachers and curriculum designers must solve.

If students are to be able to solve problems of types they have not necessarily seen before, they need the ability to transfer their knowledge and skills to new domains. Yet, most of mathematics education today focuses on Continue reading Grant Wiggins on Mathematics Education

Ten Skills Every Student Should Learn

A recent eSchool News article by Meris Stansbury lists ten skills cited by its readers as being most important for today’s students to acquire:

  1. Read
  2. Type
  3. Write
  4. Communicate effectively, and with respect
  5. Question
  6. Be resourceful
  7. Be accountable
  8. Know how to learn
  9. Think critically
  10. Be happy

The list is interesting to ponder. I would not argue that any skills on the list should be dropped, however I suspect we could have endless debates about what order to list them in or how to best group them. I am happy to note that all of the skills are beneficial in studying just about any subject or discipline.

There are a few additional skills that I would advocate adding to, or being more explicit about in the above list: