Teaching with mobile technology: seeking help!

I need your help!

Tomorrow I’m attending a conference on Education Technologies, and I will be giving a talk about using mobile technology, and social media tools, in ‘out of the classroom’ environments.  I am excited about the opportunity and I welcome the chance to discuss the topic, highlighting my field biology course as a case study.  Here’s an overview of what I will discuss:

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As part of this talk, I would like to engage a broader community of educators, using social media tools.  More specifically, if you have comments or ideas on some of the discussion questions (below), please comment on this post, or tweet at me, or use the twitter hashtag #EdTechMobile to give your perspective. (Note: For ‘real time’ interaction, you can tweet using that hashtag between 330-415 PM (Eastern) on 5 March)

Here are the discussion questions:

1) What are the challenges and opportunities when using social media tools in the classroom?

2) How might mobile technology (e.g., smartphones, tablets) facilitate learning? How might it interfere?

3) How might the approach of linking ‘out of class’ learning environments with mobile technology and social media tools be adapted for other teaching environments? (i.e., other than University-level, the context in which I have used these tools).

Thanks, everyone!

Why undergraduate students are teaching my entomology course

This term I’m teaching an introductory Entomology course at McGill. These days, however, I’m not lecturing at all – the students are doing the teaching. For the past couple of weeks, and for the next couple of weeks, groups of students are lecturing on the part of the course called ‘overview of the insect Orders‘. Typically, this section of the class is a little dry for one person to teach – it’s a standard series of lectures on the Insect Orders – and covers the  evolution, phylogeny, biology, ecology and economic importance of the Insect Orders, starting with Collembola and moving through to the ‘Big Four’ – the Lepidoptera, Hymenoptera, Diptera and Coleoptera.

This term, I decided to turn the tables, and students became the professors. They provided me ideas on what Orders they were most interested in, and based on their feedback, I assigned them to groups and scheduled who would teach what. I also provided them a detailed outline of what was expected. This is not a trivial task – preparing lectures, and lecturing, takes an incredible amount of preparation and time and energy. These lectures are graded (with a rubric), and thus in addition to the peer/instructor pressure for students, this part of the course is part of their final grade.

Here are some refections about the process, so far:

Perhaps what has struck me most with this experience is that the students are delving into the content to a level that I would not have done on my own – in part because I simply would not have the time if I was lecturing on all the Orders. The students, by becoming ‘experts’ on a topic, have more time to dig out the most interesting and fascinating facts about the Orders. They are hunting down the true controversies surrounding the systematics of different Orders, and presenting them like seasoned veterans.  They are taking ownership over the topics, and with such ownership comes responsibility, and pride.

Lecturing is so much different than the typical short-format presentations that students are used to. They have plenty of experience giving presentations to their instructors and peers, but these are seldom more than 15 or 20 minutes. Filling up 50 minutes is a very different ball game. It requires a different set of presentation skills – skills related to thinking on your feet, preparing for unanticipated questions from the audience, and experience with a more spontaneous form of science communication. In my experience, these skills are seldom developed during an undergraduate student’s academic program.

What is also evident with this process is that the students are having FUN with the content and FUN with the lectures. They are linking to the best videos and images for their Order – they are challenging each other with who can find the most fascinating facts about a particular Order. They are smiling, laughing, and genuinely passionate about what they are presenting.  They are also deeply supportive of each other – they ask good and fair questions, engage with the content, work to make the experience positive for everyone. (by the way, I have been tweeting some of the fun facts from this course using the hashtag #ENTO330 - please follow along!)

The education literature supports the ideas I have written above, and the overall process is defined as ‘peer teaching‘.  As the title of Whitman and Fife’s report states “to teach is to learn twice”  , and although caution is warranted when executing peer-teaching, that report does highlight the fact that learning can occur effectively under peer-teaching scenarios. More recent literature from Dioso-Henson (2012)  shows that “reciprocal peer tutoring” (i.e., students run tutorials instead of instructors) “produced significantly larger academic gains than traditional classroom instruction“.  Those interested in delving into the Education literature on this topic should see Topping’s (1996) article.

Now, what I have not provided here is any perspectives from the students, and Graham Scott correctly pointed this out to me. Once the course is over, I will bookend this post with another post containing some refections from students. It’s important to see whether or not my positivity is a reality from their perspective! So, stay tuned for that!

In sum, we often talk about Higher Education being about teaching and learning, with the assumption that the teaching is done by a Professor and the learning is done by the student. Peer teaching, I believe, is a valuable method by which undergraduate students can be fully immersed in the process. The learner can become the teacher and this makes the experience so much richer, for everyone.

Instructors: please contact me if you want more details on this process. I will be happy to share the details – assignment overview, grading rubric, etc.

References:

Topping, K.J. 1996. The effectiveness of peer tutoring in further and higher education: A typology and review of the literature. Higher Education 32(3): 321-345.

Dioso-Henson, L. (2012). The effect of reciprocal peer tutoring and non-reciprocal peer tutoring on The performance of students in college physics. Research In Education, 87(1), 34-49.

Whitman, N.A. & Fife, J.D. (1988). Peer Teaching: To Teach Is To Learn Twice. ASHE-ERIC Higher Education Report No. 4.

Social media, mobile technology and an outdoor classroom

Last year, my field biology course took part in an amazing project – we used mobile technology in a field setting, and combined that with social media tools.  This was done in collaboration with Teaching and Learning Services at McGill, McGill Libraries, and the tablets were generously provided by Toshiba.  I am immensely thankful for the support and an truly honoured to be able to explore these adventures in teaching and learning.  More specifically, Laura Winer, Adam Finkelstein and PhD student Crystal Ernst helped make this project a success.

One of the ‘products’ of this pilot project is this 5 minute video about using social media to engage students in inquiry-based learning:

We are continuing with these kinds of initiatives, and a Brown-Martlet Foundation grant has allowed my Department to purchase some of the tablets originally used last year. This is terrific, and as the video illustrates, the students end up benefiting.

This term, the course is again using social media, and you can find details in this post, and follow along with twitter using the hashtag #ENVB222.

Hear This! Podcasts as an assessment tool in higher education

It’s the week before classes start at McGill University. Professors are getting course outlines ready, and thinking about ways to assess students. In this post (first published over at the Inquiry Network Blog of McGill), I explore the idea of using podcasts as an assessment tool… 

As a University Professor, I’m always experimenting with new ways to assess students in my undergraduate classes. This can be a significant challenge with larger class sizes, especially since I’m not a fan of multiple choice style questions. It’s nice to be able to assess students on the basis of how they are integrating and synthesizing course content, and traditionally this is done with longer-format essay-type assignments.  These long-format assignments are great, but do take a tremendous amount of time and energy to grade, and I seldom feel I can give enough time to each written assignment.

This past winter term I was faced with an increased enrolment in my undergraduate ecology class at McGill. I had a TA for the class, but I certainly didn’t have enough TA hours to include a large individual written assignment. I started to think of new and interesting ways to grade students, and I was looking for a way to test how students might be integrating content from different lectures in the class.

This got me thinking about podcasts.  When I mow the lawn, or when I am on a long road trip I listen to a lot of podcasts, and This American Life or RadioLab have become go-to places for me to hear new and interesting stories, from science through to art and culture. A good podcast entices the listener, is creative, informative, and overall, makes learning fun.  Bingo: Makes learning fun.

Podcasts as an assessment tool seemed a perfect fit with the challenge I was facing in my ecology class.  Together with my amazing TA, Carly Ziter, we brainstormed and came up with a podcast assignment.  We assigned students to groups, and handed out the assignment. Here are some of the details, as provided to students:

The learning outcomes for the Ecology Podcast assignment are the following: (1) expose students to ecological stories in the news, (2) explore the ways that ecology is portrayed in the news media, (3) link these stories to ecological content as delivered during lectures, and (4) to communicate (orally, and as a group) the story and the ecological concepts linked to the story.  Podcasts are an exciting way to communicate science, and can be an effective tool in helping to find a deeper understanding of ecological concepts.

The Ecology Podcast is done in groups, and is devoted to exploring the portrayal of ecological concepts in the news media and linking concepts to course material. Groups are required to get approval for their topic in advance of commencing the research and recording. Within the first 10 seconds of their podcast, each student in the group is requested to clearly state their name. Introductions should be followed by the title or concept that they  discuss.  The remaining time is  spent introducing the story / concept, explaining it to the audience, and linking the story to more fundamental ecological concepts, including those discussed during lectures.  It is expected that each group member spend approximately the same time speaking on the podcast.   Students are encouraged to be creative with the podcast – to have fun, and find ways to provide an informative and entertaining podcast.  Students are encouraged to interview other experts on the topic, and find other content to bring into the podcast. Podcasts are to be between 3-4 minutes long.

The podcast assignment is worth 15% of the grade in the class, and is graded using the following rubric:

Each of the following criteria is graded between 0 (poorly done) to 5 (excellent, above expectations) for a total out of 25 points:

  1. Format & Quality (length of podcast, sound quality, all group members given equal time)
  2. Broad coverage of ecological concept (introduction and explanation of broader topic, overview of portrayal in news media)
  3. Link to fundamental ecological concepts (links to lecture content, links to other course materials)
  4. Synthesis, integration (all parts of podcast linked together, evidence of deeper critical thinking about the topic, opinions presented and discussed)
  5. Creativity (effort to make podcast interesting, fun, entertaining; evidence of creative thinking)

Carly and I also did a sample podcast (ours was on Orca whales stuck in sea ice in the Arctic). This was really fun to put together, and allowed us to refine/adjust the assignment details to ensure it would meet the learning objectives.

We also provided a list of ‘model’ science podcasts out there (e.g., Scientific America’s 60 second science podcasts, and NASA’s earth audio podcasts), as a way to encourage students to make their podcasts high quality, interesting, and effective.  Students used McGill’s Learning Management System for uploading their podcasts, and then Carly and I sat down and over the course of a day, graded the entire set of podcasts.

Overall, the students rose to the challenge and produced truly amazing and high quality podcasts. You could tell they had fun with the idea, and in many cases, the groups found ‘experts’ to interview about their topic.  Here are links to two of the podcasts, and in both cases, the students sought out and interviewed another Professor in my Department, Dr. David Bird.

This one is about cat predation on birds, and this second example is about snow geese.

From an instructor’s perspective, podcasts were a true delight to grade, and it was a refreshing change from grading essays or tests. It also allowed students to exhibit creative talents that they otherwise would not get to explore in this ecology class.  I believe the podcasts were effective at assessing how students were engaged with the course content.  Explaining ecological concepts is difficult, and requires a deep and intimate knowledge of the content. “Teaching” in the form of a podcast, is an excellent way to learn.

Podcasts were an effective form of group work. In some cases, groups could not find time to work together, so individuals were able to record sections separately and merge them together after the fact.  It’s also important to note that students had no complaints or technical issues with this assignment. They all were able to access software and hardware for this assignment, and uploading assignments to our learning management system was smooth.

In sum, podcasts are ideal as a student assessment tool, especially when class sizes make written assignments unmanageable. Podcasts are fun to put together, enjoyable to grade, and because they force an explanation of content, they can truly test content in all the right ways.

I encourage instructors to try it out — You’ll like what you hear.

Kids Like Bugs: entomology outreach in elementary schools (Part 2)

     On Wednesday, Chris Buddle and Paul Manning posted the first of a two-part series on outreach activities in elementary schools. That post focused on the ‘why’ - this one (also written by Chris and Paul) is about the ‘how’.

How to talk to kids about bugs:

First thing about talking to elementary school kids is stay calm and don’t worry!  If you have any University-level training in Entomology, you are qualified – Now, this doesn’t mean you have to be able to speak about all aspects of entomology: play to your strengths! If you are a taxonomists working on Syrphidae flies, bring in your flies and talk about them these magnificent animals.  If your experience is broader and less specialized, browse some notes, look on-line, or peek at a textbook: do a short overview of the main Orders of insects and their characteristics. Although most kids get some entomology in elementary schools, it’s not usually very much (although ALL kids do seem to learn about monarch butterflies!).

One great way to speak to kids about bugs is to make the session thematic.  In addition to bringing in a drawer or two of insects, link the specimens to biology. For example, one of us (Paul) has recently used ‘metamorphosis’ as a focal point for discussion. The transition from larvae to adult is a biological wonder, and acts as an excellent focal point for discussion. It brings together different facets of biology, from hormones, to physiological development, behavioural adaptations, through to discussion about life history strategies.  Paul brought galls into the classroom, and demonstrated that there were larvae living inside. The students screamed with excitement when they saw the larvae living within the gall. One student described it as a ‘cute white blob‘. Several students asked if they could bring the larvae home (wouldn’t Mom and Dad just LOVE that!).

Kids like bugs. And they like to draw them.

Kids like bugs. And they like to draw them.

Don’t be afraid to say “I don’t know”.  In fact, kids find it refreshing to hear that an ‘expert’ doesn’t know all the answers.  Turn it around to illustrate that the world of entomology is so vast that there are a lot of unknowns out there, and many questions still to be answered.

Have patience. With younger grades, asking kids questions, or having them answer questions, can quickly turn into ‘stories’ from young, enthusiastic students. For example:

Q: Does anyone know what kind of insect a ladybug is?

        [Hand shoots into the air...]

 A (from a 6 year old): Um, yes, I know a lot about those things.  Once, when I was 4, I remember that I saw a beautiful bug flying by my garden – it was really big and black and I think it was a ladybug and my granddad told me about how ones like that eat trees and kill the trees and that makes me sad because we have a big tree in our front yard that I really like but sometimes my little bratty brother hides behind it and scares me when I am walking by. But I really like all bugs especially ladybug ones that are red but they smell funny sometimes and my mom said they can bite – will they bite me if I play with them? why do they smell funny? why are there so many spots on them? do their spots get bigger when they grow….

Give kids a chance to tell you these stories, but know that it will take patience…. but heck, if bugs get them talking and excited, that can’t be a bad thing!

(as an aside, most elementary school teachers will typically coach students so that they will ask/answer question instead of tell stories)

Bring a few props: If you can do an event outdoors, try to bring a few sweep nets and vials.  We will often bring extra vials from the lab and give students the vials to keep (heck, plastic vials cost very little!). For MONTHS afterwards, parents will often tell us about how their child packed that vial full of insects and carried it around obsessively for weeks. That’s a great way to inspire entomology.

Beetle galleries are easily found in wood, and can be a great prop to bring to an entomology session with school kids.

If you are doing an indoor talk, make sure to have a lot of photographs of interesting insects, and whenever possible, discuss/show or use examples from your local fauna – this will allow kids to connect to things they have seen on the playground or in their own yards – this connection between the content you are discussing and the insects they are seeing on their own, is very powerful.  With a smaller group, you can certainly bring in a few drawers of insects – if you don’t have any, this becomes a great excuse to make a little synoptic collection of your own to use for educational purposes. Or, ask your local entomology museum, or local naturalist club, about borrowing some specimens.

Whenever possible, bring a few ‘real’ field guides. One of us (CB) ran a biodiversity challenge at an elementary school and managed to convince the school to buy a couple of sets of field guides. The kids LOVE the look and feel of real field guides and will thumb through them with delight. Part of our own passion about natural history can be traced back to field guides in our houses when we were young.

A field guide to insects - suitable for all ages!

A field guide to insects – suitable for all ages!

Don’t dumb down the material: Too often we think kids need to be talked down to, but nothing is further from the truth. As mentioned above, kids are sponges for information and in our experience they want to hear the details. You will want to avoid jargon, but other than that, provide the details whenever you can. Again, doing a ‘thematic’ talk with school kids becomes quite important because you just won’t have time to cover anything in-depth if you try to cover too much.

Finally, and most importantly, be passionate and enthusiastic. Kids will feel your positive energy and love of entomology; they will feed off of this, take it home with them; they will start asking more questions, start to dream, and fall further in love with the world around them. Spending a bit of time in a classroom is perhaps one of the most important kinds of outreach activities to do.

Kids Like Bugs: entomology outreach in elementary schools (Part 1)

         Written by Chris Buddle and Paul Manning.

Spending time talking to kids about Entomology is ALWAYS worth it. If ever invited to speak at an elementary school about insects, always say “yes”, and in this post, we’ll expand on why it’s worth your time. In a second post on this topic, we’ll provide some tips on how to talk to kids about bugs.  Although these posts are focused primarily at elementary school events, the ideas and tips could be expanded to community nature walks, events at an ‘earth day’ celebration, hosting a bug day in your backyard, etc.

Part 1: Why talk to kids about bugs?

Most kids aren’t afraid of nature. In our experience, elementary school kids (especially the younger grades) still have a fascination with entomology and are still curious and excited by ‘bugs’. Later in life, it seems that many kids will follow one of several paths: (a) disinterest, (b) disgust, or (c) delight. As entomologists, in a field that is so important, getting kids to be delighted is very important.

Kids like bugs.

Kids like bugs.

Kids already know a lot but they like an expert to verify their findings and support their interests. In our experience, kids can get especially excited about insects because they see them all the time – they have played with them in their yards, tasted them (perhaps), and probably spend time trying to burn them with a magnifying glass. Bugs are accessible, small, curious, and catchable, and thus kids learn about them – an entomologist can keep facilitating this learning.

Kids are truly amazed that you can ‘get a job‘ studying insects. This is unfathomable to them, since they don’t typically get much exposure to biologists. They are exposed to limited career options (“I want to play in the NHL“, “I want to be a doctor“, “I want to be a firefighter“) in part because our school systems often exclude the cool jobs like “stream ecologist”, “geologist”, or “entomologist”. The idea that you can spend time (as an adult!) collecting and curating insects (i.e., FUN STUFF) can be quite extraordinary. In our experiences, it’s so painfully obvious that working outdoors with insects is simply not noticed as a real job by many people; entomologists must work to correct this. Giving kids exposure to wonderful careers (like entomology) can help encourage future scientists that there are truly enjoyable careers that involve getting ones hands dirty, and spending time outside.

Entomologists have a responsibility to dispel myths about arthropods, and this should start at an early age. Invariably, we get statements from kids such as “My Dad told me to stay away from spiders ’cause they will bite you“, or “My aunt told me that earwigs go into your ear, so I hate them“, or “I am allergic to bees because my cousin is allergic“, etc. We can bring clarity to these kinds of statements, and by offering an ‘expert opinion’ on these topics, can help kids understand the real facts about entomology.

Kids are sponges: it is satisfying to speak to an audience who is fully engaged and willing to soak up as much as you can provide. Bugs are a very exciting topic for kids, and they will remain interested, excited and enthused if you continue to provide good content.

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Kids ask great questions.  As an example, one of us (PM) recently talked about insects to an elementary school class. The class was asked to guess what was living within a gall, and to make guesses as to what they thought the gall was, and how it was formed. After one student quickly suggested that an insect was living within the gall, a flurry of wonderful questions began. Students asked questions like:

  • How did the insect get inside the gall?
  • How does the insect survive the winter?
  • What does the insect eat when inside the plant?
  • Why doesn’t the insect kill the plant?

All of these questions prompt interesting, and relevant discussions that fit well within learning objectives in science curriculum. Providing a concrete example that is applicable to students, might also result in a better understanding of the concept.

Finally, it’s nice to talk to kids about bugs because they genuinely appreciate it. Being thanked for spending time doing this kind of outreach is really, really nice. And, sometimes you might receive some nice thank-you cards or posters to put up on your wall.  To us, these are as important as a diploma on your wall, or a favourite butterfly poster. Thank-you notes from kids are some of the most wonderful things to read, and they often include delightful, creative, and colourful drawings.

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Ecology and Mathematics: perspectives from undergraduate students

Post written by Chris Buddle and Carly Ziter (MSc student at McGill – you can follow her on twitter)

Population and Community Ecology is an introductory undergraduate course at McGill University and each lecture typically starts with an x-axis and a y-axis drawn on the chalkboard – something like this:

Chalk board, with x- and y-axis. The start of every lecture.

Chalk board, with x- and y-axis. The start of every lecture.

The course is taught from a quantitative perspective, and it uses equations, models and graphs to cover concepts ranging from logistic population growth, to metapopulation ecology and estimating species diversity.  The class uses Gotelli’s “A Primer of Ecology” as the text – a book that walks through many ecological concepts from first principles. It includes calculus, probability theory, statistical distributions, and null models.

It was therefore fitting that the ‘E.O. Wilson versus Math” debate was discussed during lecture last week.  Students were asked to read Wilson’s piece in the Wall Street Journal, and read some of the blog posts that reacted to this, including Jeremy Fox and Brian McGill‘s posts on dynamic ecology. Students were also asked to look at some of Terry McGlynn’s writing over at small pond science, and to come to lecture prepared – to have opinions and be willing to discuss these opinions.

For those not fully aware of this debate, here it is in a nutshell: Wilson argued that a ‘deep’ understanding of math may not always be prerequisite for doing great science, or at least may not be required for generating big ideas and concepts. Wilson was in part trying to encourage people who are ‘math phobic’ that this phobia needs not be a reason to stay out of science.  Not surprisingly, this stirred up a lot of debate (and some of it was rather harsh!), and the debate was particularly interesting from the perspective of Ecology since this discipline has always struggled with this topic (see Terry’s excellent post about tribalism in ecology for some perspectives on this).

Here is a summary of the key points that were discussed during lecture – and let’s just say that a 50 minute lecture slot was NOT enough time for this topic! (by the way, there were between 50 and 60 students who attended this  lecture, and the class is comprised primarily of students studying environmental biology).

Many of the students were surprised at the tone and overall discussion points that emerged from Jeremy Fox’s post – they argued that when they read Wilson’s piece, they didn’t feel the intended audience was ‘established’ ecologists – but rather the post was meant for students at the start of their careers. Some of them found the blog posts way over the top, and the academic discussions took away from the main message.  Some felt that Wilson was arguing in part about the need for freedom to think without any boundaries (mathematics, or anything else).  Creative thought need not be constrained, and students coming up through the system, whether they are math literate or not, should never fear heading into science (indeed, some confessed that an increase in math courses may have driven them away from biology altogether).  Related to this, mathematical models all require assumptions (we talked a LOT about this when working through Gotelli’s book!), and any assumptions are limiting and could distract from thinking out of the box about any topics, including ones that are ecological. These students worried that the constraints imposed by math could force ecologists to view the world through a particular lens.

That being said, many of the students also agreed that a deeper understanding of mathematics was absolutely required for ecology – especially since the world is complex, with complex problems – problems that require multiple disciplines to solve.  However, while these disciplines include mathematics and biology, they also include literature, history, environmental policy, and more.  What a solid argument! And it was great to see that argument expressed by 20 year-olds.  Yes, math is important, but it is one tool that we need in this world, and it’s not necessarily more important than other tools.  While some ecologists are strong in math, others may prefer to hone their policy skills, for example. Ecology’s strength, in part, is in its ability to bridge different disciplines and students expressed how ecology is actually a ‘great uniter’ of biology and math (and other fields, certainly some areas of ecology draw upon a range of ideas from sustainability science, medicine, economics, history, etc).

The students also expressed concern about how mathematics is taught, from elementary school all the way to University – they expressed how learning mathematics in isolation of other topics is ‘ok’ for individuals with an intuition and natural ability with math – but many students felt that a better way to learn about math was applying it to the ‘real world’. The application of mathematics is the best route to learn mathematics. Ecology was again touted as a perfect example of a discipline in which application of mathematics is clear – from predicting distribution of invasive species to modelling species richness in fragmented forests.  For some students, math was not a subject they initially enjoyed, or strove to learn – it was ultimately through their study of ecology that they began to value math as a tool they could use to support their discoveries, and lend credibility to their work.

By in large, students agreed that mathematics was required for ecology, but there was certainly debate about how much was enough – whether it was enough to use mathematics as a tool, or that perhaps mathematics was more like a language.  A language in which fluency is required so all the nuances can be understood and that the full meaning is in place.  From those advocating mathematical “fluency”, there was a strong opinion that like languages, mathematics can be learned with hard work and focus (yes, they agree with Wilson on this point!) – this opinion comes with a wealth of experience in the classroom at McGill since many of the students are mother-tongue French and have learned English after coming to McGill.  In other words, if you can learn a language you can also learn math.

The final argument put forward by students was that this entire discussion about Ecology was from a very narrow perspective – what about the role of traditional ecological knowledge?  Ecology is a much older discipline than Clements, von Humbolt, Haeckel, or even Aristotle. Throughout history, humans have been interacting with their environment, and have been observing nature.  By this act, humans have been counting, developing models, and making predictions… for thousands of years.  Linking mathematics to nature is very, very old.  Ecologists ought to pay more attention to other ways of looking at the natural world, other ways to visualize, predict, observe and count. Although this is certainly not the same kind of math as presented by Gotelli, perhaps it could be as insightful.

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In sum, the discussion with undergraduate students on this topic was insightful, fascinating and important. There was clearly a strong appreciation for the role of mathematics in ecology, but also different ideas about the degree to which a deep understanding of math is required – which often related back to the students own struggles with, or aptitude for, math earlier in their studies. It was validating to hear that they appreciated using Gotelli’s book to learn the foundations of ecology, and recognized that ecological models can be both limiting and liberating.