Survey of algebraists

 

How many years have you been teaching upper division mathematics courses?

m  1-2 years (1)

m  3-6 years (2)

m  More than 6 years (3)

 

What is your job title?

 

How many times have you taught an abstract algebra course

m  1 to 4 times (1)

m  5 to 8 times (2)

m  8 or more times (3)

 

Which best describes the abstract algebra courses you teach most often: 

m  an abstract algebra course designed for undergraduate or graduate mathematics education students (1)

m  an introductory group and/or ring theory course for undergraduate mathematics majors (2)

m  an introductory graduate level course for master's or PhD math students (3)

m  a graduate level course with a graduate level abstract algebra pre-requisite course (4)

m  some other course in abstract algebra (5) ____________________

 


 

What is the terminal mathematics degree offered at your institution? 

m  Associates Degree (1)

m  Bachelor's Degree (2)

m  Master's Degree (3)

m  PhD (4)

 

When teaching ${q://QID43/ChoiceGroup/SelectedChoices}, do you teach groups then rings or rings then groups?

m  Groups first (including equivalence relations) (1)

m  Rings first (2)

m  I only teach rings (3)

m  I only teach groups (4)

m  Some other order (5) ____________________

 

In your department, is there a proof-writing class that students take prior to taking ${q://QID43/ChoiceGroup/SelectedChoices}?

m  Yes, it is a pre-requisite course (1)

m  Yes, it is an optional course (2)

m  No (3)

 

In your department, is there a mandatory or optional abstract algebra course that follows ${q://QID43/ChoiceGroup/SelectedChoices}?

m  Yes, it is required for math majors (1)

m  Yes, it is optional (2)

m  No (3)

 

When you teach ${q://QID43/ChoiceGroup/SelectedChoices}, do you teach it as a capstone course?

m  Yes (1)

m  No (2)

 

Approximately what percentage of your students take this subsequent course?

 

In the last term that you taught ${q://QID43/ChoiceGroup/SelectedChoices}, what was the approximate grade distribution (by percentage)?

______ A (1)

______ B (2)

______ C (3)

______ D/F/Withdraw (4)

 

While teaching ${q://QID43/ChoiceGroup/SelectedChoices}, approximately how many times per class meeting do you: 

 

None (1)

1 or 2 (2)

3 or more (3)

pause and ask students if they have questions (1)

m   

m   

m   

have students engage in small-group discussions or problem-solving (2)

m   

m   

m   

use visual and/or physical representations of groups and group elements (3)

m   

m   

m   

use diagrams to illustrate ideas (4)

m   

m   

m   

have students ask each other  questions (5)

m   

m   

m   

include informal explanations of formal statements (6)

m   

m   

m   

 

 

While teaching ${q://QID43/ChoiceGroup/SelectedChoices}, what is the approximate amount of time per class that you are:<div><br></div>

 

Never (1)

0-25% (2)

25-50% (3)

50-75% (4)

75-100% (5)

showing students how to write specific proofs (1)

m   

m   

m   

m   

m   

having students work with one another in small groups (2)

m   

m   

m   

m   

m   

having students work individually on problems or tasks (4)

m   

m   

m   

m   

m   

having students give presentations of completed work (3)

m   

m   

m   

m   

m   

lecturing (5)

m   

m   

m   

m   

m   

holding a whole-class discussion (i.e., a discussion where students speak and respond to each other) (6)

m   

m   

m   

m   

m   

having students explain their thinking (7)

m   

m   

m   

m   

m   

 

 

While teaching ${q://QID43/ChoiceGroup/SelectedChoices}, approximately how many times per term do you:  

 

Once per term or not at all (4)

Infrequently, maybe a couple times per month (3)

About once per week (5)

About once per class meeting (2)

More than once per class meeting (1)

have students present a proof (or counter-examples) to the class (1)

m   

m   

m   

m   

m   

have students develop their own definitions (2)

m   

m   

m   

m   

m   

have students develop their own conjectures (3)

m   

m   

m   

m   

m   

have students develop their own proofs (4)

m   

m   

m   

m   

m   

lead discussions in which students discuss why material is useful and/or interesting (5)

m   

m   

m   

m   

m   

 

 

<p>If you lecture while teaching ${q://QID43/ChoiceGroup/SelectedChoices}, how frequently does your instruction (either lecture or tasks) include the follwing?</p>

 

Never (1)

Rarely (a couple times a semester) (2)

Sometimes (approximately once or twice a month) (3)

Often (approximately once a week) (4)

Frequently (5)

The definition of a concept (1)

m   

m   

m   

m   

m   

Examples of a construct (2)

m   

m   

m   

m   

m   

Statement of a theorem (3)

m   

m   

m   

m   

m   

Examples related to a theorem (4)

m   

m   

m   

m   

m   

The proof of a theorem (5)

m   

m   

m   

m   

m   

Examples that support a proof or pieces of it (6)

m   

m   

m   

m   

m   

Applications of a theorem and/or construct (7)

m   

m   

m   

m   

m   

Calculations to show operations in a new system or demonstrate procedures (e.g., decomposing a n-cycle into 2-cycles; Euclidean algorithm) (8)

m   

m   

m   

m   

m   

Proof verification (9)

m   

m   

m   

m   

m   

Counter-examples to a theorem or definition (10)

m   

m   

m   

m   

m   

Explanations of the history or rationale for a particular definition (11)

m   

m   

m   

m   

m   

Explanations of the rationale for and evolution of a particular theorem (12)

m   

m   

m   

m   

m   

 

 

While teaching ${q://QID43/ChoiceGroup/SelectedChoices}, how frequently do your students spend class time on the following (meaning, they're working alone or together on these without your explanation):

 

Never (1)

Rarely (a couple times a semester) (2)

Sometimes (approximately once or twice per month) (3)

Often (approximately once per week) (4)

frequently (5)

Developing a definition or exploring it's evolution (1)

m   

m   

m   

m   

m   

Developing examples and/or counter-examples of a construct (2)

m   

m   

m   

m   

m   

Developing or explaining a theorem (3)

m   

m   

m   

m   

m   

Developing examples and/or counter-examples relating to a theorem (4)

m   

m   

m   

m   

m   

Developing or critiquing a proof (including proof-verification) (5)

m   

m   

m   

m   

m   

Developing examples that support or instantiate a proof (6)

m   

m   

m   

m   

m   

Working with applications of theorems or constructs (7)

m   

m   

m   

m   

m   

Doing calculations (e.g., decomposing n-cycles into 2-cycles; Euclidean algorithm) (8)

m   

m   

m   

m   

m   

 

 

Chose the appropriate level of agreement with the following items:

 

Disagree (1)

Slightly Disagree (2)

Slightly Agree (3)

Agree (4)

I think lecture is the best way to teach (1)

m   

m   

m   

m   

I think lecture is the only way to teach that allows me to cover the necessary content (2)

m   

m   

m   

m   

I think students learn better when they do mathematical work (in addition to taking notes and attending to the lecture) in class (3)

m   

m   

m   

m   

I think students learn better when they struggle with the ideas prior to me explaining the material to them. (4)

m   

m   

m   

m   

I think students learn better if I first explain the material to them and then they work to make sense of the ideas for themselves (5)

m   

m   

m   

m   

I think there’s enough time for all the content I need or want to teach (6)

m   

m   

m   

m   

I think that all students can learn advanced mathematics (7)

m   

m   

m   

m   

I think all students can learn abstract algebra (8)

m   

m   

m   

m   

When I last taught algebra, I had enough time during class to help students understand difficult ideas (9)

m   

m   

m   

m   

When I last taught algebra, I felt pressured to go through material quickly to cover all the required topics (10)

m   

m   

m   

m   

 

 

How strong is your interest in:

 

Very Strong (1)

Strong (2)

Weak (3)

Very Weak (4)

Teaching abstract algebra (1)

m   

m   

m   

m   

Teaching other advanced classes (2)

m   

m   

m   

m   

Discussing/reading about how students learn key ideas in abstract algebra (3)

m   

m   

m   

m   

Doing research in abstract algebra (4)

m   

m   

m   

m   

Doing/reading research that could be considered the scholarship of teaching and learning (5)

m   

m   

m   

m   

 

 

If you wanted to make changes to the course you teach, do you believe you would have the following support from your department/college: 

 

Yes (1)

Maybe (2)

No (3)

Time to plan and redesign your course that would be supported and valued in your annual review or P&T process (1)

m   

m   

m   

Travel support to attend professional development opportunities (e.g., Project NExT) (2)

m   

m   

m   

Freedom to make changes to the content of your course (e.g., including or excluding certain topics and/or textbook changes) (3)

m   

m   

m   

 

 

<p>Do you feel pressure from your department to cover a fixed set of material in your abstract algebra course? </p>

m  Yes (1)

m  No (2)

 

Do you feel like your job requirements allow you to spend as much time as you would like on teaching and preparing for class (including improving courses)?

m  Yes (1)

m  No (2)

 

How influential are the following on your teaching? 

 

Not at all (1)

Somewhat (2)

Very (3)

Reading PRIMUS, MAA Notes volumes on teaching (1)

m   

m   

m   

Talking to colleagues about teaching specific content (2)

m   

m   

m   

Reading math education research literature such as RUME proceedings (3)

m   

m   

m   

Reading about teaching tips and techniques (4)

m   

m   

m   

Going to talks, workshops, or conferences about teaching (e.g., MathFest mini-courses, SOTL sessions, …) (5)

m   

m   

m   

New curricula materials (e.g., textbooks or other published materials) (6)

m   

m   

m   

Blogs and social media (7)

m   

m   

m   

Participating in communities like Project NExT (8)

m   

m   

m   

Observing colleagues teach (9)

m   

m   

m   

Being involved with projects with mathematics education researchers (10)

m   

m   

m   

Your own experiences as a student (11)

m   

m   

m   

Your own experiences as a teacher (12)

m   

m   

m   

 

 

What source of information is the single most influential on your decisions about teaching abstract algebra?

 

On the left we provide several topics that may be included in a <b>first semester, introductory undergraduate abstract algebra course</b>. Please rank them in terms of priority <b>for your idealized introductory course </b>by dividing the topics into the three categories on the right.  

Topics I always teach

Topics I try to teach

Topics I do not cover or would not want to cover

______ Groups and Subgroups (1)

______ Groups and Subgroups (1)

______ Groups and Subgroups (1)

______ Group Isomorphisms (2)

______ Group Isomorphisms (2)

______ Group Isomorphisms (2)

______ Group Homomorphisms (3)

______ Group Homomorphisms (3)

______ Group Homomorphisms (3)

______ Quotient Groups (4)

______ Quotient Groups (4)

______ Quotient Groups (4)

______ Lagrange's Theorem (5)

______ Lagrange's Theorem (5)

______ Lagrange's Theorem (5)

______ Fundamental Homomorphism Theorem (6)

______ Fundamental Homomorphism Theorem (6)

______ Fundamental Homomorphism Theorem (6)

______ Rings (7)

______ Rings (7)

______ Rings (7)

______ Fields (8)

______ Fields (8)

______ Fields (8)

______ Field Extensions (9)

______ Field Extensions (9)

______ Field Extensions (9)

______ Ring Isomorphisms (10)

______ Ring Isomorphisms (10)

______ Ring Isomorphisms (10)

______ Ring Homomorphisms (11)

______ Ring Homomorphisms (11)

______ Ring Homomorphisms (11)

______ Polynomial Rings (12)

______ Polynomial Rings (12)

______ Polynomial Rings (12)

______ The Sylow Theorem(s) (13)

______ The Sylow Theorem(s) (13)

______ The Sylow Theorem(s) (13)

______ Proof-writing (including counter-examples) (14)

______ Proof-writing (including counter-examples) (14)

______ Proof-writing (including counter-examples) (14)

______ Proof-reading and comprehension (15)

______ Proof-reading and comprehension (15)

______ Proof-reading and comprehension (15)

______ Conjecturing (the process of developing and refining conjectures) (16)

______ Conjecturing (the process of developing and refining conjectures) (16)

______ Conjecturing (the process of developing and refining conjectures) (16)

______ Defining (the process of writing definitions) (17)

______ Defining (the process of writing definitions) (17)

______ Defining (the process of writing definitions) (17)

______ Instantiating (18)

______ Instantiating (18)

______ Instantiating (18)

 

 

What text do you use and why did you choose to use it (including if you wrote your own)?

 

Approximately how long have you been using your current text (including previous editions)?

 

<p>How satisfied are you with your textbook? Please give some explanation.</p>

 

Have you ever taught abstract algebra in a non-lecture format?

m  I currently do (1)

m  I have in the past, but I currently lecture (2)

m  No (3)

 

How would you characterize your non-lecture approach? 

q  Moore Method (including Modified Moore) (1)

q  Inquiry-based (2)

q  Problem-based (3)

q  Other (4) ____________________

 

Did you work with people to help implement this approach (e.g., <span style="font-family: Arial, Helvetica, Verdana, sans-serif;">The Academy of Inquiry Based Learning</span> or Project NExT)? If so, who (or none)? 

 

Did you create your own course materials or use/modify curriculum materials (e.g., TAAFU by Sean Larsen or IBL materials)?

 

Would you ever consider teaching abstract algebra in a non-lecture format? Or, if you used to but no longer do now, would you consider doing so again?

m  Yes (1)

m  No (2)

 

Why wouldn't you?

q  I need to cover a certain amount of content and I can only do that by lecturing (1)

q  My classes are too big for it to be viable (2)

q  It's not appropriate at my institution (3)

q  It's not appropriate for my students (4)

q  I don't have the support from my department needed to implement that sort of change (5)

q  I think it would go poorly (6)

q  Other (7) ____________________

 

Why haven't you?

q  I haven't had time to redesign my course (1)

q  I haven't found materials that I like (2)

q  I don't have the support of my department needed to implement that sort of change (3)

q  I don't know where to start (4)

q  Other (5) ____________________

 

How satisfied are you with your students' learning?  Please give some explanation.