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Questions tagged [assessment]

Assessment questions ask how to properly, effectively, and efficiently ascertain the abilities of students. This doesn't necessarily involve numerical grades, but rather is focused on an overall characterization of knowledge/ability.

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61 votes
4 answers
6k views

Is it worth grading calculus homework?

I am a young math educator. I've TAed four semesters of calculus for various instructors. Some instructors have required me to grade selected problems in homework sets. Another required me simply to ...
abnry's user avatar
  • 852
44 votes
4 answers
3k views

Teaching undergraduates who expect a high-school-like learning environment

tl;dr: Some students expect to be told "what's on the test", to memorize and then move on. What can be done to change how they learn while teaching them what to learn? Context: Introductory, ...
Brendan W. Sullivan's user avatar
36 votes
4 answers
2k views

How to convey the meaning of "mathematical maturity"?

Some university-level courses have no specific prerequisites, yet are mathematically involved to the extent that someone with little to no experience in math will probably find themselves in over ...
Adam Bjorndahl's user avatar
32 votes
8 answers
2k views

How to solve the problem of Wolfram Alpha?

I teach to predominantly non-majors in college algebra, precalculus, and calculus. How can one possibly incentivize or rationalize assigning practice problems outside of class when this software is ...
goruda's user avatar
  • 423
28 votes
4 answers
1k views

The Undergraduate Responsibility Gradient

We tell undergraduate students that they should study two to three hours for every hour they spend in class. We know that many students don't follow through with this nearly to the degree that they ...
Jon Bannon's user avatar
  • 6,173
24 votes
2 answers
783 views

Separating the roles of "teacher" and "assessor"

Teachers at the university level (at least what I've seen in the US) are responsible for both teaching students the material for a course, and assessing the students' understanding of the course ...
Mike Pierce's user avatar
  • 4,845
22 votes
2 answers
759 views

Exam philosophy

I'm curious if anyone knows of any books, studies, or other resources on the philosophy of creating and grading mathematics exams. After working as a graduate TA for 4 years and dealing with a wide ...
icurays1's user avatar
  • 485
21 votes
1 answer
739 views

How do I track down the sources of solutions which students have used to cheat on exams?

I recently taught an introduction to real analysis. I assigned a (covid-induced) take-home final, which included the question: Define the set S by $$ \bigcup_{n=1}^\infty \left\{ \frac{a}{2^n}\...
Anthony Quas's user avatar
20 votes
5 answers
649 views

Making standards for "showing work" explicitly clear to students

I do not mean for this thread to be a discussion of whether or not students should show work on an exam, whether they should be docked points for just "seeing" an answer and writing it down, whether ...
Brendan W. Sullivan's user avatar
20 votes
3 answers
617 views

Requiring basic skills to pass a course without increasing their grading weight

As I grade my final exams, I sometimes find calculus 1 students who will pass with a C but lack critical skills like the chain rule. This can be for a number of reasons, for instance: They understand ...
Chris Cunningham's user avatar
19 votes
5 answers
398 views

Is required reading of the text effective, and how can it be assessed?

This will likely depend on the class, of course. But I've asked calculus students in the past if (a) they regularly read the textbook and (b) whether this is helpful for them and (c) whether they like ...
Brendan W. Sullivan's user avatar
19 votes
5 answers
405 views

Can homework play a substantial role in the assessment of understanding in university math?

Ideally, I'd like my students' grades to be based on more than just exams, because I think that certain tasks, such as writing proofs, aren't best performed in a test environment. Using homework for ...
N. W. Clerk's user avatar
17 votes
6 answers
5k views

How to deal with a "protest" assignment?

I just received one assignment (by email) from a student. Out of 6 questions, "I don't know" is the answer to 4 of them. There is also a comment at the end of the assignment which suggests my ...
user avatar
17 votes
2 answers
515 views

Is there a math curriculum that is aware of CAS and the internet?

About 15 years ago, I heard a math education professor give a talk about how computer algebra systems would change the kinds of questions teachers would ask high school and first year college students....
Noah's user avatar
  • 1,016
17 votes
2 answers
261 views

What happens when the state mandates college math placement policies?

The state of Illinois is currently considering a bill to mandate that all public institutions accept a score of 3 on every Advanced Placement exam. Bill here. The lobbyists in favor of the bill claim ...
Chris Cunningham's user avatar
16 votes
2 answers
1k views

What are some resources for "ungrading" in a math class?

Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...
Mike Pierce's user avatar
  • 4,845
16 votes
3 answers
594 views

How to balance between teaching to the standardized test vs understanding?

For people teaching high school standardized curriculums such as AP, IB, or A-Levels, how do you find the balance between preparing students for the standardized test compared to ensuring they ...
okzoomer's user avatar
  • 341
15 votes
2 answers
259 views

How can you determine the quality of your teaching, or someone else's?

The question in the title is immensely subjective and broad, and so I would like to narrow it to an answerable question: What measures are in common use by administrators and researchers in ...
Brian Rushton's user avatar
13 votes
3 answers
3k views

What research is there on the effectiveness of multiple choice questions for summative assessment?

This is perhaps the question that some thought Grading scale: how to handle multiple choice questions with different number of choices really was. I'm of the opinion that multiple choice questions ...
Andrew Stacey's user avatar
12 votes
4 answers
7k views

Grading homework problems on completion vs. correctness, and overall grading

I taught Calculus 2 at my institution the past two semesters and several students have left comments in their course evaluations that advocate grading homework problems based on whether they were ...
Brendan W. Sullivan's user avatar
12 votes
4 answers
923 views

How to design multiple choice questions

I've seen the previously-asked questions about the effectiveness of multiple choice problems, but I want to know about design. What are best practices in multiple choice problem design? The "common" ...
Nick C's user avatar
  • 9,729
12 votes
2 answers
263 views

How do you incorporate the results from a final exam into evidence of learning in a valid and justifiable way (i.e. grade determination)?

How do you incorporate the results from a final exam into evidence of learning in a valid and justifiable way (i.e. grade determination)? This question is open to all education levels. What is your ...
Marian Minar's user avatar
12 votes
1 answer
474 views

How, now, shall we teach math online?

Now that everyone has had the experience of teaching math in an online/remote/synchronous/asynchronous format, and looking forward to more of this in the Summer and Fall terms, how do we change our ...
Nick C's user avatar
  • 9,729
12 votes
1 answer
2k views

elementary level assessment tools

I'm looking for an assessment tool to ability group 4th and 5th grade students, in particular setting a "top" group. This group would receive more enrichment, less practice on concepts and a faster ...
Marjorie 's user avatar
11 votes
9 answers
4k views

Effectiveness of Requiring Students to Repeat Proofs Presented in Class

In teaching mathematics, I've avoided asking students to replicate proofs I've demonstrated in class, believing this approach primarily tests memorization rather than understanding or critical ...
user avatar
11 votes
3 answers
407 views

In math courses with writing requirements, how should large papers be graded fairly?

In a course I am teaching this semester, I am required to have my students write a large (6-12 page or so) paper worth 40% of their grade. Many other colleges have courses with similar requirements, e....
Brian Rushton's user avatar
10 votes
4 answers
427 views

Placing incoming college freshmen: basic algebra, pre-calc, calc

Assume that you have incoming college freshmen, so you might have access to their high school courses and grades, as well as their results on a placement test offered by your college. Also, assume ...
Brendan W. Sullivan's user avatar
10 votes
2 answers
368 views

Pros and cons of randomised question generation

I am developing an assessment piece where the content is the same but the particular numbers are different for each student. It involves finding Triangle Centers given points using coordinate geometry....
pdmclean's user avatar
  • 967
10 votes
2 answers
2k views

Project/Assessment based on Flatland for Secondary Geometry Class

One of my favorite books is Flatland by Edwin Abbott, which is incredibly rich in geometric concepts especially relating to dimensionality. I would really like to assign it to my secondary geometry ...
celeriko's user avatar
  • 5,070
10 votes
2 answers
172 views

Cognitive demands of a mathematical task

I'm looking for a theoretical framework to classify a task based on its cognitive demand. I only have the Smith and Stein's (1998) proposal and PISA framework such as my principal references. In ...
Carlos Torres's user avatar
10 votes
4 answers
331 views

Is it a good idea to use past questions in examinations?

When it comes to writing examinations, there are two options I am considering. Write the entire exam originally (which will of course mean some well-known proofs, thereby technically not making it ...
Trogdor's user avatar
  • 1,106
10 votes
2 answers
483 views

Weekly quizzes as an alternative for midterms? What is this called?

I have seen (by some of my former instructors) the following strategy applied as an alternative to traditional "midterms and final" assessment in a math course: Students take a quiz weekly. ...
Opal E's user avatar
  • 4,089
10 votes
1 answer
210 views

How to read better?

In this semester I've realized that many of the problems (my) students have can be solved by reading better. The most recent example I've encountered was in the last exam; I asked them the following: ...
Ana Galois's user avatar
10 votes
1 answer
1k views

Effectiveness of multiple-choice versus short answer questions

I want to know if there is any research on whether students' learn better by answering selected response (multiple choice) questions than constructed response (written) questions. My gut feeling is ...
Mark Fantini's user avatar
  • 3,040
10 votes
2 answers
511 views

Placement tests for middle school math

Our district has changed its approach to placing students in grades 6 and 7 math classes. Students considered for placement above grade level must now take a test composed of problems drawn from the ...
Kate's user avatar
  • 101
9 votes
7 answers
2k views

Do you have an efficient way to view student responses to remote assignments allowing them to type math symbols and steps? (Middle + High school)

Asking for a friend, this seems generally useful given #distanceLearning right now. Below is her message in a quote block followed by my response. I am using Google Classroom, G-sheets, G-Docs, G-...
E_Rushton's user avatar
  • 179
9 votes
4 answers
280 views

How to assess an undergraduate mathematics program?

Our university and department, like most, are required to "assess" our program annually. In the past our department has done this by e.g. picking one of the learning outcomes for our program and a ...
Mike Shulman's user avatar
  • 6,580
9 votes
3 answers
4k views

Questions for Oral Examination in Mathematics

I am working on some research on implementation of oral assessment in mathematics classroom, and I was wondering are there any questions/problems/concepts in mathematics that can be only assessed ...
Milica's user avatar
  • 91
9 votes
2 answers
150 views

What do you look for in a student presentation?

Context: I am teaching a course on plane geomtery at an mid-size state University in the USA for students who wish to be high school math teachers. They will have to make presentations once per week, ...
David Steinberg's user avatar
9 votes
2 answers
476 views

Should we assess ability to use specific problem solving methods, or general ability to solve problems?

This is my first semester being an instructor of record for a college algebra course. One of the sections we cover is "methods of solving quadratic equations", where we discuss factoring and ...
Brain Gainz's user avatar
8 votes
6 answers
4k views

Would you correct grading mistakes downwards if there is a mistake in grading?

In a recent exam, I give student a true or false question asking them to decide if a statement is true. After the grades have been published, a student pointed out that I misread the statement and ...
LeafGlowPath's user avatar
8 votes
5 answers
398 views

Mathematics exam -- How to keep brain functioning through a four-hour exam?

So my question isn't directly related to math, but I think you might be able to help me. I'm a 17 year old, last year at school. My class specializes in math/physics (that's our educational system in ...
user494951's user avatar
8 votes
4 answers
2k views

Seeking Advice on Allowing Students to Skip a Quiz in Linear Algebra Course

I am currently teaching a linear algebra course at a university and have chosen to assess my students using five quizzes throughout the semester, instead of assigning homework. I have encountered a ...
user avatar
8 votes
1 answer
115 views

Assessing the level of students in a class

Recently I've moved to another university and next semester I will have my first class there. The problem is that I don't know the level of the students that will be attending my class. Of course, I'...
dtldarek's user avatar
  • 8,957
8 votes
0 answers
193 views

Are there standard questions for testing how an instructor grades calculus?

My institution is now in the process of "standardizing" our calculus classes. One issue we have is the variation among instructors in grading problems. I am interested if there are ways to objectively ...
Matt Brenneman's user avatar
7 votes
6 answers
1k views

Efficient methods to receive and grade online mathematics assessments?

I am UK-based but I guess this issue currently affects all maths educators and has probably been addressed by those how have been delivering courses through online channels for the past few years. ...
Clive Long's user avatar
7 votes
4 answers
403 views

Teaching arithmetic operations ($+ - \times \div$) to a 3 year old

What is the best way to teach the standard arithmetic operations ($+ - \times \div$) to a 3 year old child? Also: How we do know if the child has really understood it? can a kid be 3 years old ...
Vishal's user avatar
  • 187
7 votes
4 answers
1k views

How to standardize grading across several sections of a course?

Suppose you're the instructor of a large university course split into several sections, each of which has a TA. (Think of a giant lecture-style calculus course with several hundred students that meet ...
Brendan W. Sullivan's user avatar
7 votes
2 answers
260 views

How can PISA released questions be used to improve the mathematical competencies of students?

The purpose of this question is to ask for your experiences using PISA released questions at classroom. How do you use them to improve the mathematical competencies of your students? How do you ...
Charo's user avatar
  • 331
7 votes
1 answer
317 views

Measure of Improvement in Math Skills from Remediation with ALEKS

I am analyzing some data on ALEKS for my home institution (ALEKS, an acronym that stands for "Assessment and Learning in Knowledge Spaces", is an online tutoring and assessment program that includes ...
Matt Brenneman's user avatar