General Chemistry covers a wide variety of structure-property relationships that rely upon electronic, atomic, crystal or molecular structure. Often these submicroscopic factors come into conflict: What has a higher boiling point, methanol or hexane? What atom has a larger radius, Li or Mg? O or Cl? A good strategy to address these “conflicting factors” is giving students experimental data at different points of the learning sequence and allow them to identify the patterns as well as identify the limit of predictability of such patterns.

“*ChemEd X Data*” is a web interface developed by the author (http://chemdata.r.umn.edu/, J. Chem. Educ, 2014, 91, 1501). This tool was designed for chemistry students to navigate, filter and graphically represent chemical and physical data. It can assist students at identifying trends in structure-property relationships, they can create controlled experiments to test a relationship as well as investigating how different molecular factors may affect a single macroscopic property. In particular, since the site offers unstructured but dynamically searchable data, it is designed to have students learn control of variable strategies (CVS) which are activities that require self-regulation and self-evaluation skills for its successful completion.

In this paper, students complete a common sequence of activities related to structure-property relationships using *ChemEd X Data* at different points of a General Chemistry semester. Student performance is analyzed through a common sequence of questions in different topics with the objective of understanding which activities require a higher cognitive skill, as well as identify the type of student background that correlates with success in the activities and in the course in general.

## Comments

## mathematical software for students of chemistry

There was a lack of understanding by some participants about the nature of the interactive electronic textbook Mathematics for Chemistry with Symbolic Computation; the fact that it is interactive and electronic necessitates the embedding of this book within, or compatible with, a particular software.

If I were at this time contemplating the production of such a book, on assessing the available software, free or costly, forsymbolic computation, I should choose Maple because its capabilities for the stated purpose, including its specially designed Student packages, greatly exceed those of any other available software, and its learning

curve is less steep than that of other software. Since my first use of computer algebra in 1973 (Formac on IBM 360/50 computer), I have become acquainted with no less than ten separate programs, or languages, for computer algebra, and in 1982 I published, in journal Computers and Chemistry, the first paper describing the applications of computer algebra in chemistry (although others had used computer algebra methods for such chemical purposes even as early as 1954). I respectfully submit that I might be satisfactorily qualified to make the preceding assertions.

Incidentally, in viewing some promotional material from Maplesoft, the producer of Maple product as advanced mathematical software, I notied a news item about pupils in Tasmania aged 11 years being taught calculus with Maple.

https://www.maplesoft.com/company/casestudoes/stories/136487.aspx

Although such an activity is evidently possible, I personally advocate not teaching calculus until the post-secondary stage of education.

Moreover, some participants might have the impression that I am somehow part of a marketing strategy on behalf of Maplesoft. Again, I advocate the use of free software Geogebra in schools, available in several languages, to emphasize the teaching of algebra and geometry at that level, although there is no harm in using Maple for instructional purposes at that level in an enlightened manner.

## Recurring themes in the paper discussions

Looking back at the comments folks made concerning the six papers of this Spring 2018 newsletter, I wanted to collect some of the themes we discussed (in no particular order)

## Learning curve

The computer-based tools ranged from fairly simple and focused to all-purpose symbolic and numerical computation engines. Strategies for helping students to learn working with these tools without distracting too much from learning chemistry included written manuals, video, integrating manual and assignments within the tool, and writing an entire textbook within the tool. The amount of setup also varied, from having to install software on your computer to pre-installed software to using tools in an internet browser. Finally, there were examples of using web-based entry points (SageMathCell, Rstudio) instead of a program installed on the own computer.

## Scope of tool

In some projects, tools were used for a single session or topic. Others spanned the entire semester or course sequence. The present tools were used in the lab, in the class, for homework assignments or in multiple settings. The question was raised whether students could make use of the tool outside of the course where they learned it, making the effort put into learning the mechanics of it more worthwhile.

## Open educational resources

Many of the tools were available for free to all. Sometimes, there was support from the institution to obtain campus-wide licences for software, sometimes not. In one case, making local materials available to others depended on institutional support. In other cases, folks used existing open source mechanisms (such as posting a permanent link to materials within SageMathCell) to disseminate materials.

## Role of math courses

There were multiple comments about moving math instruction from the typical math sequence to more applied math, either by working with mathematicians, or by teaching it within chemistry. (This reminds me of a model I know from the physics curriculum in Germany: While physics students take formal and rigorous math courses in the math department, there is also a math-supplement to the intro physics course that gives a quick-and-dirty introduction to the calculus they need to appreciate and work with Maxwell's equations - the math curriculum is too slow because it has to deal with all the special cases that don't occur in nature.)

## Pedagogical flexibility

When you have a computational system (such as PQtutor, SageMath, R or Maple) available, you have a choice as a teacher whether to focus on a math or statistics step, or treat it as a known recipe (or black box, if it was not introduced yet). What you choose will depend on where the students are at, and what your learning goal is for that particular day. There was a nice example of using R to give a partial solution where you just plug in your experimental data, or leaving it up to the student to generate the necessary code.

## How to teach problem solving

We dipped into the question how to learn solving quantitative problems. How do you provide sufficient information upfront without giving away the answer? How do you transition from studying worked examples to having students work out a problem on a blank sheet of paper? What are the strategies to optimize use of the limited working memory we have available? We discussed the role of graphs in visualising concepts or trends in data, and the role of open-ended problems in grasping magnitudes of various quantities.

## Transferable computer skills

We discussed how the computer skills students aquire in one course transfer to other courses or to tasks they face after graduation. One model is to commit to a certain software and use it across the curriculum. Another model is that students independently go back to tools they learned in one course, and apply it elsewhere (this only works if they still have the tool available). Finally, it is possible that students pick up general computer literacy or even computer science skills which will help them to use other tools in other courses, and more sophisticated tools ("professional software" instead of "learning software") or a wider range of features in a given tool.

## Thank you for the summary

Karsten, that is a very nice summary of this newsletter. I must confess that I did not intend the newsletter to have a thematic sequence, but I think it worked very well due to the quality of the contributing authors and commentors.

I'm going to save what you wrote here and share it with our chemistry and mathematics faculty. You have succinctly captured range of topics and potential teaching strategies that we have been discussing in recent years.

Jason

## With and Without Technology

Karsten and Jason --

Karsten’s was a nice summary indeed!

The question of problem of “teaching problem solving” (and what scientists who study how the brain works say about it) my personal interest. One of the counter-intuitive findings of cognitive research is that pre-grad-school students cannot solve problems by applying generalized “critical thinking” or “reasoning” strategies the way a “10-year expert” in a field can do. These generalized approaches, as Karsten referenced, tend to quickly overwhelm the limits of working memory when dealing with non-memorized relationships.

Instead, to solve a problem of any complexity, says the science, the student must “fluently, intuitively, and often subconsciously recall memorized facts and procedures that they have successfully used in previous problem solving.” As cognitive scientist Daniel Willingham puts it, “Understanding is nearly always remembering in disguise.”

The way to gain fluency, say the cognitive folks, is first to move relationships and procedures into memory, and then to use procedures to solve problems in different contexts, to “conditionalize” or “contextualize” or “situate” them (terms dependent on who is summarizing the research).

One of the implications is, when using software to solve mathematics, there are usually choices that the user must make, and choosing correctly often depends on knowing how the problem would be solved, if the numbers were simple, without the software.

I don’t think I’ll get much argument from the presenters and this audience that students need to know how to apply procedures to complex algorithms without the technology, when the numbers are contrived to lend themselves to mental math. But I do think this argues for emphasizing problem solving without much technology in science courses in the first two college years, and technology use in later courses only after problems contrived to illustrate how the math works are mastered without the technology first. Dr. Penn’s paper in the fall ConfChem, where physical chemistry was taught pretty much without calculators, and students praised the approach (by the END of the course), I think speaks to this.

I certainly have enjoyed our fall and spring discussion of the oft-neglected quantitative side of our quantitative science!

-- Eric (rick) Nelson

## technology and problem-solving

There are ways to assist in the "moving of relationships and procedures into memory" using technology in the form of web activities. I have been experimenting with this for years (bestchoice.net.nz). In my experience (and from my data) students have much more difficulty with the thinking behind the problem than the calculation.

## Deep vs. Surface Learning

Well spoken, Rick! And I will add this excellent caveat to our discussion of problem-solving re: memorization, conceptual understanding, and the affective domain, whether using pencil & paper, or technology:

https://podnetwork.org/content/uploads/V21-N8-Rhem.pdf

W. Cary Kilner