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## Gradebook

### Request for comments: Gradebook 2.x architecture

Request for comments: Gradebook 2.x architecture
Hi folks,

please note that there is an ongoing discussion of the Gradebook internal improvements that might have significant impacts on the Gradebook usage. We believe that the changes we are thinking about would bring useful features for advanced Moodle users while simple usage would remain simple.

There is a draft specification document at http://docs.moodle.org/en/Development:Gradebook_2.x_architecture that summarizes the planned changes. Now we would like to get a feedback from the community to see what you think of it. Thank you for constructive and thoughtful comments in advance.
The myth of the default (Re: Request for comments: Gradebook 2.x architecture)

We are inclined to assume that defaults make it easier for the average user. This maybe true in many cases but not all.

IMO, the first problem of the gradebook even for a simple usage is that by default, evey activity with a grade is pushed into it. But in many cases many activities are for practice, often more than those which are for the course grade. This behavior overloads the gradebook with items that shouldn't be there. All solutions which involve states and degrees of visibility miss the point.

So, if this is not already in the developing spec, I suggest that the gradebook should start blank and the simple user will be able to add to it only the desired items (or select and add all items), just like adding questions to a quiz page (the principle, not the interface).

A possible approach for adding grade items is to use only manual grade items but make the manual grade items such that they may be set up to be based on a grade from an activity.

Re: The myth of the default (Re: Request for comments: Gradebook 2.x architecture)

I would love to see this addition - if the activity could have the option of adding to the gradebook yes or no - that would be great.  I do hope that this one is added to the list of additions to the gradebook.  Thank you so very much.

Re: The myth of the default (Re: Request for comments: Gradebook 2.x architecture)

Thank you Nancy. Your suggestion to add an option to the activity could work too. But consider this. In most cases, whatever you do in the activity settings with respect to the gradebook, you still have to go to the gradebook and make some adjustments. And in most activities the settings form is already overloaded and quite confusing, not to say intimidating, as it is. So perhaps instead of adding the option to the activity you could just go to the gradebook and select to add the activity grade item from a dropdown list. Instructors who do not use the gradebook (there should be quite a few) would have a simpler activity settings form to work with. Just a thought.

Grades appearance (Re: Request for comments: Gradebook 2.x architecture)

This refers mainly to The grades appear in the gradebook immediately. I don't know if this will address all the issues with grades appearance but it seems to me that instead of ultra complex state machine to control grades inclusion or exclusion in aggregations, a simpler approach could be to allow the user to create more than one grades view. So, one view could be accumulative grade, another could reflect the actual course grading scheme, a third just raw grades etc. With the existing show/hide/until functionality, instructors would be able to control which views to make available to students and when.

Re: Grades appearance (Re: Request for comments: Gradebook 2.x architecture)

The gradebook supports multiple view - the different gradebook reports.

At the moment, all these different views display data from a single central data model. All the different activities feed data into that model, and the manually entered grades are stored there. The aggregations are computed within the model.

Therefore, having different views that display different aggregations would be difficult. The view would have to re-compute the aggregates with different settings. Not impossible though.

Re: Grades appearance (Re: Request for comments: Gradebook 2.x architecture)

From a user's perspective, in the course level there is only one view/report with two display styles, horisontal (the grader report) and vertical (the user report). This one view/report represents one way of aggregating the grades in the course.

To illustrate, this is like organizing the grades in one Excel worksheet and looking at this worksheet either as is or transposed. But with Excel I can add another worksheet with different columns and different aggregations of the same grades, and I can use this other worksheet either as read-only or read-write.

I haven't looked under the gradebook's hood so I take your word for it that the aggregations are static and not recaculated upon display (if that's indeed your word for it). Having different views that display different aggregations would not be difficult if the aggregations were recaculated upon display, right? Is there a substantial overhead?

Re: Grades appearance (Re: Request for comments: Gradebook 2.x architecture)

Allowing some room for my misunderstanding of what's being asserted, it is my opinion that aggregations for categories and course total are calculated on the fly.  I have looked under the hood and see that everytime the grader report is refreshed, generate_grades() is called and when it hits a category or course item, aggregrate_grades() is called.  The only exception to this is if Sum of Grades agg method is used.

Re: Request for comments: Gradebook 2.x architecture

Some courses feel the need for allotting a combined grade for all members of a group in a group activity. I don't know if this is to be incorporated in the assignment module or in the gradebook.

Kindly consider!

-Radhika

Re: Request for comments: Gradebook 2.x architecture

One one purely practical level, I have a request about the API for activities to pass grades to the gradebook. At the moment, the activity has to build an array userid => grade to pass to the update_grades function.

In the quiz, it would actually be easier for me (and potentially much higher performing) if I could call the API with the SQL for a query that returns a result set with two columns, userid, and grade.

See https://github.com/timhunt/Moodle-Question-Engine-2/blob/qe2_wip/mod/quiz/locallib.php#L614 (yuck, who wrote that long rambling method ). Focus, in particular, on the $finalgradesubquery bit in the middle. Re: Request for comments: Gradebook 2.x architecture Do we really need the complexity of the approval conditions? What about a single boolean flag in the grade item (is_released) that external events can toggle? I suppose the danger is two competing external things trying to toggle it. E.g. the quiz trying to hide it because it is set not to display grades until after the close date, while the teacher keeps trying to manually open the eye in the gradebook. Re: Request for comments: Gradebook 2.x architecture I guess I'd think that in 95% plus conditions the approval is the grade itself. The approver is the one awarding the grade or setting up the module to award an appropriate grade. 100% agree this is unnecessary added complexity. This approval architecture doesn't address the single most-common scenario we encounter, "I want to see a running calculation of my grade to-date". This is pretty well met with the current gradebook and a couple tweaks to allow for extra credit in all agg methods. Re: Request for comments: Gradebook 2.x architecture I don't think it is a 'Problem' that teacher and students see different things in the gradebook. It is essential that teacher can quickly see raw grades as they come in before they are released to students. And I think with the new data model, it is easy to achieve that, and letting Teachers also know what students will see. There is a bit of careful work needed to ensure that the state of everything is clear from the UI, but the back-end will have all that state information readily available to be displayed in whatever way we work out is the best way to display it. Re: Request for comments: Gradebook 2.x architecture Brief points: • Storing all grades and settings in the gradebook, not the module, is good - providing there are good developer docs. I have never really understood what I should be doing in the quiz code. It has largely been monkey-see-monkey-do copying code from other modules • I don't see any problem with storing grades <0 or >1. Re: Request for comments: Gradebook 2.x architecture Another technical API point: Should we take the display of grades (as %, Float, scale, etc) out of the core gradebook code, and have a new, very simple sort of plugin grade/formatter. That would be a subclass of a grade_formatter_base with a single format_grade method. It is interesting to think about what arguments that method would need: format_grade($grade, $max,$isfinal, ...)

Re: Request for comments: Gradebook 2.x architecture

I am really unconvinced by the need for pluggable gradebook engines. It seems like unnecessary complexity. You only have one example of why it might be needed, and that could easily be handled by one configuration option that the core grade calculation code uses.

Re: Request for comments: Gradebook 2.x architecture

Hello,

I forwarded your proposal to some of our faculty that use the grade book heavily. Here is a response I got:

It looks as if they are working on some important improvements.  The idea of having grades not show up until after they have all been entered is a good one, but part of a bigger issue that entering grades directly into Moodle (for a class of 60, for instance) is clunky and more time consuming that entering them in EXCEL and the importing them into the gradebook - but I don't see why this should necessarily be true.
Re: Request for comments: Gradebook 2.x architecture

I work with classes of 360 and I assure you with all the issues the gradebook may have, entering grades directly into Moodle isn't one. If your faculty are comfortable with Excel they should keep using it, and when the grades are ready to be published, they can import all the grades and feedback directly into the gradebook, by a few additional clicks. In many cases this method is by far more efficient than working directly on Moodle, even with small classes of 60, and regardless of what UI Moodle may introduce (I'd love to here why your faculty find this method clunky and time consuming). This also effectively resolves the issue that all grades should be made available online at the same time.

I do a lot of work directly on Moodle but I still do substantial work in the background in Excel and other apps, not only grades but also content (e.g. quiz questions). This not only makes my work more efficient but also my own backup file and means for transfering content from one year and its Moodle server to another without depending on adminatration services.

hth

Re: Request for comments: Gradebook 2.x architecture

I'm Sharon's faculty colleague who finds it unfortunate that it isn't easier to enter grades directly into Moodle.  I use the same "few additional clicks" to upload grades from EXCEL - but by the time I've chosen the wrong format by mistake, and then go back to take out the extra line at the bottom of the EXCEL spreadsheet where I calculated an average grade but that was causing problems with uploading, and then upload again, this time successfully uploading the grades, and then repeat the whole upload process yet again in order to upload the comments associated with new grade items, and then I have to go in and tell Moodle what category the new grade items are in, and what the total points are, it has taken 10 minutes.  And I'd rather spend those 10 minutes on something else.

And I could, if Moodle had a simple interface for entering grades for one particular item so that I didn't have to use EXCEL (by simple I mean that every grade requires three keystrokes: two digits and ENTER key, and no mouse movement, and above all, no autofill that fills in "100" if I type 1/ENTER).

Re: Request for comments: Gradebook 2.x architecture

I respectfully submit that the main problem with the gradebook as it stands is that it is NOT SIMPLE.  I've read through the (sparse) architectural specification which introduces an even more complex back-end with the assumption that its complexities can be hidden from the user through a well-programmed UI.  I've seen no evidence to-date that Moodle HQ-driven gradebooks have been able to successfully hide the complexities of the gradebook back-end.  Having read all postings to date it seems a great many of them would agree that a lot of the suggested "improvements" are unnecessary complexity added in.

IMO, the best gradebook interfaces have come from community-driven initiatives.  Yet... I see that word, "internal" in your first sentence which reminds me of the "delete everything upon unenrollment" fiasco.  I'd encourage you to bring the whole discussion out into the community -- data model, etc.  The people who understand best how the gradebook is used are out here and able to intelligently comment on the whole picture.

Re: Request for comments: Gradebook 2.x architecture

Sorry to be so contrary but all of this doesn't make a whole lot of sense from where I sit.  The kind of issues our schools (used to) have are with:

1. Aggregations: hardly anybody knows what it means and fewer how it works.  Why are there so many agg types.  We've limited it to three and are seriously considering limiting it to one -- Simple.  Because...
2. Weighting: is so easily misunderstood.  Every grade has a weight -- either imputed by the teacher in the "weight" column (if using Weighted agg) or the grademax (if using anything else).  If Sum of grades is fixed (which we've done) to allow inclusion of only graded items in its calculation and categories are allowed to accumulate maxes from children (which we've done) so they accurately represent the weight of the category before alteration, then "Simple" is the only agg method required, IMO. Allowing the default weight to be changed gets you "Weighted".
3. Enormous confusion with nested course item/category/item layout of grader report.  Flattening that out made a big difference in ease-of use.  Categories and their children are color-coded in the headers.    The ability to expand and contract categories (what a confusing interface) was absolutely not needed when we implemented a two-way scrollable interface so students and grade headers were always visible on the report.  Also eliminated those pesky mouseovers. Would be nice to be able to drag or move items around on the grader report though from category to category
4. Too much to edit in a big grader report is a real problem, fixed long ago by LSU with their "Quick grading" columns and rows.
5. What the student sees.  We made all the columns configurable for the user report and included some that weren't there before (weight, average, points (real, but cummulative), percentage, letter).  Teachers easily turn off what they don't want their students to see.

All of this has been in use by our schools for four terms or more.  I don't know what kind of uptake others have but we put up 850 courses a term and have no mandate that teachers need to use Moodle.  70% of the instructors use Moodle for at least one of their courses.  96% of the students use it for at least one courses.  Of that total, 236 courses used the gradebook.  I think that's a good percentage given the circumstances and I attribute it to students driving their teachers to know where they stand at all times and some slight fixes for a gradebook that's only kinda broken.  Nicholas did an amazing job given the pressure he was under and the diverse audiences he was trying to satisfy.  All-in-all the gradebook calculates accurately -- its just too complex for most people to use as it is.

Re: Request for comments: Gradebook 2.x architecture

I bet you haven't limited your teachers' Excel with all its aggregation functions, right? Excel is much more complex than the Moodle gradebook, and yet many who are lost in Moodle gradebook are comfy with Excel. Why? Because, to begin with, in Excel they can add only the few columns they need for the aggregation. But in Moodle they get everything else from the site and soon lose track of the few required columns. So they need to start using categories which they don't really need, and complex aggregation method so as to exclude these categories or individual items, and even formulas. And all they wanted is the sum of 4 grade items...

The solution is quite simple. Don't push anything into the gradebook. It should be like Excel. You go there and you add only what you need.

Re: Request for comments: Gradebook 2.x architecture

I think that teachers' adeptness with Excel is due to its familiar methods from their years of experience using it for grade management.  The mechanics of spreadsheet management have remained pretty consistent for most of their careers.  The Moodle grading interface has very different mechanics from Excel, so there is very little skill transfer.  It is a new skill that must be acquired.  I think that what a lot of teachers want, though it would be difficult to develop, is an embedded spreadsheet in Moodle that would behave like Google Apps, with familiar mechanics.

Re: Request for comments: Gradebook 2.x architecture

The Moodle grading interface is indeed different from Excel but not the very different and the grading mechanics is pretty much the same. I don't have any particular problem with either the interface of the mechanics but then again I'm probably highly skilled in these sorts of things. I only suggest that Moodle's pushing items into the gradebook is one thing too many and althoug this is done out of pure good will, it only backfires. It may perhaps be less pure but do more good, if Moodle will let the user pick which goes in and which stays out.

Re: Request for comments: Gradebook 2.x architecture

I can get along with the concept of adding only the grade items you want into the gradebook and leaving the rest off on the side somewhere.

Re: Request for comments: Gradebook 2.x architecture

Bob - you mention, "we implemented a two-way scrollable interface so students and grade headers were always visible on the report." -- Does this exist in Moodle 2.3?

Re: Request for comments: Gradebook 2.x architecture

Yes, our "grader report" freezes grade item headings and the student information column(s) so only the table of values scrolls -- both ways.  It is called the LAE Grader (LAE standing for Liberal Arts Edition) and is available from CLAMP (Collaborative Liberal Arts Moodle Project), an organization of 30+ schools (almost all higher ed) in North America.  The report is used by many (I hear from folks all over the world), does not change the calculations (though it provides for displaying accurate point totals if you desire) and is available for 1.9 and 2.x.

Re: Request for comments: Gradebook 2.x architecture

One more comment before I go to sleep.  There has always been talk about a "centralized" grading interface so quizzes and assignments, etc, don't keep their own grades.  That talk's gone on forever but nothing ever came of it so with very little ingenuity we altered mod/assignment/index.php to allow manual input of decimal grades and push them directly into the gradebook.  If configured accordingly it will even ignore gradebook overrides (how much value did we get out of all that confusion?) so a teacher can update their grade from the gradebook or from the assignment interface and they don't really even need to know there's a difference (which some of them don't).  That's 1.9 though.  Its been in use for over a year and available in the tracker as a patch but gets ignored everytime another point release comes out.  I'm not going to waste time finishing the 2.0 mods until we're ready to implement 2.0 unless someone from Moodle HQ gives some indication that the effort would be worthwhile beforehand.

Different capabilities

This is not really related to the new architecture (I think) but just a comment:

- At present there are separate capabilities for grading within each type of module, e.g. mod/quiz:grade.

- It would be possible to change this to use a standard 'can you grade this' capability.

- Such a change would have advantages (shortens capability list, may simplify permissions) and disadvantages (cannot set up roles so that by default they can grade only certain types of thing).

I don't actually have an opinion either way - this just came up because I am specifying an enhancement that adds grading support to some OU custom modules. The current approach is to add new capabilities, which I'm doing; but Tim suggested I should post here to mention it.

--sam

Re: Request for comments: Gradebook 2.x architecture
I have read the draft specification and all the comments here. I somewhat appreciate the debate on the architecture but feel others are more qualified to lead that debate. From a practitioners point of view, the grade book 'appears' challenging to most moodle course practitioners facilitators. The coverage of the grade book a strength for power users, off putting for novices. Second, our staff outlined they only discovered the grade book towards the end of process course design process, rather than incorporating grade book design as part of the course design process, (effectively using the grade book then became a secondary training concern for us) My reflection is that grade books would be more readily used if somehow incorporated / highlighted into resource / activity creation. Eg Add to grade book YES/NO. Second, there is an opportunity to raise the profile of the gradebook demonstrate to course facilitators by making a submission count or information a usable feature. Terminology changes from 1.9 to 2 have been well received (eg page), is there a case within the grade book too?
Re: Request for comments: Gradebook 2.x architecture

After giving my reading further time to digest, there is one further point I would like to open to discussion.

The relationship between the course facilitator and the student and their assignment / activity submission.

Currently we use the assignment submitted block to notify work waiting to be graded. Can this aspect of the gradebook be brought within the core functioning (if it is not already?)

Re: Request for comments: Gradebook 2.x architecture

Hi David,
Is this post meant to discuss the list posted in the draft spects document, or are you open to considering and adding more features?
I do have a list as well

Re: Request for comments: Gradebook 2.x architecture

I would say don't forget those of us (many in the UK if not elsewhere) who do not use grades in the the way Moodle assumes.  I do absolutely nothing in any of my (full time) teaching which awards a percentage grade or any other way of monitoring levels.  I use only criteria-based assessment.  The student has either done it or not.  I am currently trying to use outcomes to monitor this sort of progress but currently the only way for a student to monitor their progress against those outcomes is the gradebook and that gets very cluttered and confusing.

TBH it doesn't matter whether the student passes an activity or not (especially learning activities) what matters is whether any outcomes covered by that activity are met.  This gets more confusing when outcomes could be met in just one of a choice of activities.  Perhaps rather than squeezing outcomes into the gradebook a dedicated outcome monitoring module is needed and then people with criteria-based assessment methods could just ignore the gradebook.  If not then grading needs to become a lot more flexible and inclusive.

Re: Request for comments: Gradebook 2.x architecture

I would like to second Martin's point about criteria-based assessment.  While I appreciate that an attempt to allow for criteria-based assessment has been made with Moodle Outcomes, it really isn't granular enough to provide the kind of information that would make criteria-based assessment manageable for most teachers (in the upper K-12 grades - I can't speak for the elementary level).  To really track whether a student has met the required criteria (or Standards and Benchmarks in US lingo), it would be necessary for a teacher to be able to assign one or more criteria to every assessment question (not just every overall assessment), and then generate reports that would display student performance relative to each criteria.  If that data could be captured, some really helpful information could be made available to teachers, students, parents, and administrators (e.g. - the student's mean performance relative to each criteria, the student's best performance relative to each criteria, the student's most recent performance relative to each criteria, whether each criteria has been adequately assessed).  There is a huge push toward K-12 criteria-based assessment in the US, and the single biggest obstacle to implementing it is that it is extremely time consuming to do manually.  I suspect that the only real means of making criteria-based assessment practical for teachers is via an LMS that builds the data from the assessments themselves (rather than manually evaluating all student assessments - formative and summative - and inputting them into a spreadsheet or stand alone grade book program).  I have been considering trying my hand at writing a module that would accomplish this, but if those more talented than I would consider adding this functionality to the grade book (and all forms of Moodle assessment tools) that would be even better.  I really think this is a major issue for K-12 schools, and I don't see any platform/program out there addressing it.


text:
This article is written like a personal reflection, personal essay, or argumentative essay that states a Wikipedia editor's personal feelings or presents an original argument about a topic. Please help improve it by rewriting it in an encyclopedic style. (October 2018) (Learn how and when to remove this template message)

"Natural kind" is a label to which scholars have assigned incompatible meanings. Some treat it as a classification identifying some structure of truth and reality that exists whether or not humans recognize it. Others treat it as a human classification of knowings that work instrumentally.

Every "kind" is a generalization grouping certain characteristic traits. It consists of a general class and of individual examples of the class. As formulated by Aristotle, the essence of every thing humans can know exists as an unconditional abstract kind or species: (1) "all water [kind] is ${\displaystyle H_{2}O}$ [trait]"; (2) "All men are mortal"; (3) "All ravens are black."[1]: 419–24

Today, few scholars endorse Aristotle's formulation, but many continue to suppose that natural kinds are the structure of truth and reality. They may appear as units of scientific hypotheses, generalizations, and theories. Identification of their traits appears illogical, since it is practically impossible for inductive reasoning to rest on observation of "all" examples of characteristic traits. But it appears necessary to draw inductive inferences about kinds after observing a few examples. Inductive kinds often "work" as predicted—no exceptions to the classification are found—justifying belief in immutable natural kinds[2]

This article presents conflicting meanings of natural kind. John Dewey held a minority view that belief in unconditional natural kinds is a mistake, a relic of obsolete scientific practices. W. V. O. Quine and Hilary Kornblith held the still-reigning view that natural kinds are the unchanging structure of truth and reality. Hilary Putnam rejects descriptivist approaches to natural kinds with semantic reasoning. Hasok Chang and Rasmus Winther hold the emerging view that natural kinds are useful and evolving scientific facts.

## John Dewey

In 1938, John Dewey published Logic: The Theory of Inquiry. He there explained how modern scientists create kinds through induction and deduction, and why they have no use for natural kinds.

The philosophical issue is how humans can dependably predict that unobserved examples of a kind will have the same traits as a few observed examples. The traditional answer grew out of Aristotle's assertion that humans describe things they know in two kinds of propositions. Existential kinds—known by observing traits—are stated in "generic" propositions. Conceptual kinds—known by intuitive recognition of groups of traits—are stated in "universal" propositions.[1]: 529–32

Dewey argued that modern scientists do not follow Aristotle in treating inductive and deductive propositions as facts already known about nature's stable structure. Today, scientific propositions are intermediate steps in inquiry, hypotheses about processes displaying stable patterns. Aristotle's generic and universal propositions have become conceptual tools of inquiry warranted by inductive inclusion and exclusion of traits. They are provisional means rather than results of inquiry revealing the structure of reality.

Propositions as such are ... provisional, intermediate and instrumental. Since their subject-matter concerns two kinds of means, material and procedural, they are of two main categories: (1) Existential [generic means, known by induction], referring directly to actual conditions, as determined by experimental observation, and (2) ideational or conceptual [universal means, known by deduction], consisting of interrelated meanings, which are non-existential in content ... but which are applicable to existence through the operations they represent as possibilities.[1]: 283–4

Modern induction starts with a question to be answered or a problem to be solved. It identifies problematic subject-matter and seeks potentially relevant traits and conditions. Generic existential data thus identified are reformulated—stated abstractly as if-then universal relations capable of serving as answers or solutions: If ${\displaystyle H_{2}O}$, then water. For Dewey, induction creates warranted kinds by observing constant conjunction of relevant traits.

No grounded generic propositions can be formed save as they are the products of the performance of operations indicated as possible by universal propositions. The problem of inference is, accordingly, to discriminate and conjoin those qualities [kinds] of existential material that serve as distinguishing traits (inclusively and exclusively) of a determinate kind.[1]: 275

Dewey used the example of "morning dew" to describe these abstract steps creating scientific kinds. From antiquity, the common-sense belief had been that all dew is a kind of rain, meaning dew drops fall. By the early 1800s the curious absence of rain before dew and the growth of understanding led scientists to examine new traits. Functional processes changing bodies [kinds] from solid to liquid to gas at different temperatures, and operational constants of conduction and radiation, led to new inductive hypotheses "directly suggested by this subject-matter, not by any data [kinds] previously observable. ... There were certain [existential] conditions postulated in the content of the new [non-existential] conception about dew, and it had to be determined whether these conditions were satisfied in the observable facts of the case."[1]: 430

After demonstrating that dew could be formed by these generic existential phenomena, and not by other phenomena, the universal hypothesis arose that dew forms following established laws of temperature and pressure. "The outstanding conclusion is that inductive procedures are those which prepare existential material so that it has convincing evidential weight with respect to an inferred generalization.[1]: 432  Existential data are not pre-known natural kinds, but become conceptual statements of "natural" processes.

Objects and qualities [kinds] as they naturally present themselves or as they are "given," are not only not the data of science but constitute the most direct and important obstacles to formation of those ideas and hypotheses that are genuinely relevant and effective.[1]: 425
We are brought to the conclusion that it is modes of active response which are the ground of generality of logical form, not the existential immediate qualities of that which is responded to.[1]: 252

Dewey concluded that nature is not a collection of natural kinds, but rather of reliable processes discoverable by competent induction and deduction. He replaced the ambiguous label "natural kind" by "warranted assertion" to emphasize the conditional nature of all human knowings. Assuming kinds to be given unconditional knowings leads to the error of assuming that conceptual universal propositions can serve as evidence for generic propositions; observed consequences affirm unobservable imagined causes. "For an 'inference' that is not grounded in the evidential nature of the material from which it is drawn is not an inference. It is a more or less wild guess."[1]: 428  Modern induction is not a guess about natural kinds, but a means to create instrumental understanding.

## Willard Van Orman Quine

In 1969, Willard Van Orman Quine brought the term "natural kind" into contemporary analytic philosophy with an essay bearing that title.[3]: 1  His opening paragraph laid out his approach in three parts. First, it questioned the logical and scientific legitimacy of reasoning inductively by counting a few examples posting traits imputed to all members of a kind: "What tends to confirm an induction?" For Quine, induction reveals warranted kinds by repeated observation of visible similarities. Second, it assumed that color can be a characteristic trait of natural kinds, despite some logical puzzles: hypothetical colored kinds such as non-black non-ravens and green-blue emeralds. Finally, it suggested that human psychological structure can explain the illogical success of induction: "an innate flair that we have for natural kinds.[4]: 41

He started with the logical hypothesis that, if all ravens are black—an observable natural kind—then non-black non-ravens are equally a natural kind: "... each [observed] black raven tends to confirm the law [universal proposition] that all ravens are black ..." Observing shared generic traits warrants the inductive universal prediction that future experience will confirm the sharing: "And every reasonable [universal] expectation depends on resemblance of [generic] circumstances, together with our tendency to expect similar causes to have similar effects." "The notion of a kind and the notion of similarity or resemblance seem to be variants or adaptations of a single [universal] notion. Similarity is immediately definable in terms of kind; for things are similar when they are two of a kind."[4]: 42

Quine posited an intuitive human capacity to recognize criteria for judging degrees of similarity among objects, an "innate flair for natural kinds.” These criteria work instrumentally when applied inductively: "... why does our innate subjective spacing [classification] of [existential] qualities accord so well with the functionally relevant [universal] groupings in nature as to make our inductions tend to come out right?"

He admitted that generalizing after observing a few similarities is scientifically and logically unjustified. The numbers and degrees of similarities and differences humans experience are infinite. But the method is justified by its instrumental success in revealing natural kinds. The "problem of induction" is how humans "should stand better than random or coin-tossing chances of coming out right when we predict by inductions which are based on our innate, scientifically unjustified similarity standards."[4]: 48–9

A standard of similarity is in some sense innate. This point is not against empiricism; it is a commonplace of behavioral psychology. A response to a red circle, if it is rewarded, will be elicited by a pink eclipse more readily than by a blue triangle; the red circle resembles the pink ellipse more than the blue triangle. Without some such prior spacing of qualities, we could never acquire a [classification] habit; all stimuli would be equally alike and equally different.[4]: 46

Quine credited human ability to recognize colors as natural kinds to the evolutionary function of color in human survival—distinguishing safe from poisonous kinds of food. He recognized that modern science often judges color similarities to be superficial, but denied that equating existential similarities with abstract universal similarities makes natural kinds any less permanent and important. The human brain's capacity to recognize abstract kinds joins the brain's capacity to recognize existential similarities.

Credit is due to man's inveterate ingenuity, or human sapience, for having worked around the blinding dazzle of color vision and found the more significant regularities elsewhere. Evidently natural selection has dealt with the conflict [between visible and invisible similarities] by endowing man doubly: with both a color-slanted quality space and the ingenuity to rise above it.
He has risen above it by developing modified systems of kinds, hence modified similarity standards for scientific purposes. By the [inductive] trial-and-error process of theorizing he has regrouped things into new kinds which prove to lend themselves to many inductions better than the old.[4]: 49
A man's judgments of similarity do and should depend on his theory [universal propositions], on his beliefs; but similarity itself, what the man's judgments purport to be judgments of, [is] an objective relation in the world. It belongs in the [generic] subject matter not of our [universal] theory ... about the world, but of our [universal] theory of the [generic] world itself. Such would be the acceptable and reputable sort of similarity concept, if it could be defined.[4]: 53

Quine argued that the success of innate and learned criteria for classifying kinds on the basis of similarities observed in small samples of kinds, constitutes evidence of the existence of natural kinds; observed consequences affirm imagined causes. His reasoning continues to provoke philosophical debates.

## Hilary Putnam

In 1975, Hilary Putnam rejected descriptivist ideas about natural kind by elaborating on semantic concepts in language.[5][6] Putnam explains his rejection of descriptivist and traditionalist approaches to natural kinds with semantic reasoning, and insists that natural kinds can not be thought of via descriptive processes or creating endless lists of properties.

In Putnam's Twin Earth thought experiment, one is asked to consider the extension of "water" when confronted with an alternate version of "water" on an imagined "Twin Earth." This "water" is composed of chemical XYZ, as opposed to H2O. However, in all other describable aspects, it is the same as Earth’s "water." Putnam argues that the mere descriptions of an object, such as "water," is insufficient in defining natural kind. There are underlying aspects, such as chemical composition, that may go unaccounted for unless experts are consulted. This information provided by experts is what Putnam argues will ultimately define natural kinds.[6]

Putnam calls the essential information used to define natural kind "core facts." This discussion arises in part in response to what he refers to as "Quine’s pessimism" of theory of meaning. Putnam claims that a natural kind can be referred to via its associated stereotype. This stereotype must be a normal member of the category, and is itself defined by core facts as determined by experts,. By conveying these core facts, the essential and appropriate use of natural kind terms can be conveyed.[7]

The process of conveying core facts to communicate the essence and appropriate term of a natural kind term is shown in Putnams example of describing a lemon and a tiger. With a lemon, it is possible to communicate the stimulus-meaning of what a lemon is by simply showing someone a lemon. In the case of a tiger, on the other hand, it is considerably more complicated to show someone a tiger, but a speaker can just as readily explain what a tiger is by communicating its core facts. By conveying the core facts of a tiger (e.g. big cat, four legs, orange, black stripes, etc.), the listener can, in theory, go on to use the word "tiger" correctly and refer to its extension accurately.[7]

## Hilary Kornblith

In 1993, Hilary Kornblith published a review of debates about natural kinds since Quine had launched that epistemological project a quarter-century earlier. He evaluated Quine's "picture of natural knowledge" as natural kinds, along with subsequent refinements.[3]: 1

He found still acceptable Quine's original assumption that discovering knowledge of mind-independent reality depends on inductive generalisations based on limited observations, despite its being illogical. Equally acceptable was Quine's further assumption that instrumental success of inductive reasoning confirms both the existence of natural kinds and the legitimacy of the method.

I argue that natural kinds make inductive knowledge of the world possible because the clustering of properties characteristic of natural kinds makes inferences from the presence of some of these properties to the presence of others reliable. Were it not for the existence of natural kinds and the causal structure they require, any attempt to infer the existence of some properties from the presence of others would be no more than quixotic; reliable inductive inference would be impossible. The [generic] causal structure of the world as exhibited in [universal] natural kinds thus provides the natural ground of inductive inference.[4]: 7

Quine's assumption of an innate human psychological process—"standard of similarity," "subjective spacing of qualities"—also remained unquestioned. Kornbluth strengthened this assumption with new labels for the necessary cognitive qualities: "native processes of belief acquisition," "the structure of human conceptual representation," "native inferential processes," "reasonably accurate detectors of covariation."[4]: 3, 9. 95  "To my mind, the primary case to be made for the view that our [universal] psychological processes dovetail with the [generic] causal structure of the world comes ... from the success of science.[4]: 3

Kornblith denied that this logic makes human classifications the same as mind-independent classifications: "The categories of modern science, of course, are not innate."[4]: 81  But he offered no explanation of how kinds that work conditionally can be distinguished from mind-independent unchanging kinds. .

If the scientific categories of mature sciences did not correspond, at least approximately, to real kinds in nature, but instead merely grouped objects together on the basis of salient observable properties which somehow answer to our interests, it would be utterly miraculous that inductions using these scientific categories tend to issue in accurate predictions. Inductive inference can only work ... if there is something in nature binding together the [generic] properties which we use to identify kinds. ... Unobservables [universal propositions] are then postulated to explain the constant conjunction of observable properties.[4]: 41–2
We approach the world by presupposing that it contains natural kinds. Our inferences depend on this presupposition,... This presupposition thus gives us a built-in advantage in understanding what the world is like, and thereby makes inductive understanding of the world a real possibility.[4]: 87
When a population [kind] is uniform with respect to some [generic] property, [inductive] inferences from small samples, and indeed, from a single case, are perfectly reliable. If I note that a [generic] sample of [universal] copper conducts electricity and straightaway conclude that all copper conducts electricity, then I will do just as well as someone ... checking a very large number of copper samples for their conductivity.[4]: 92–3, emphasis added

Kornblith didn't explain how tedious modern induction accurately generalizes from a few generic traits to all of some universal kind. He attributed such success to individual sensitivity that a single case is representative of all of a kind.

If we are sensitive to the situations in which a population is uniform with respect to some property, then making inferences on the basis of very small samples will be a reliable and efficient way to gain information about a population [natural kind].".[4]: 93  He argued that even human infants are intuitively sensitive to natural classifications.  :    "From the beginning, children assume that the natural world is divided into kinds on the basis of underlying features which are responsible for their superficial similarities, and that these similarities are an uncertain guide to that real underlying structure."[4]: 9

Accepting intuition as a legitimate ground for inductive inferences from small samples, Kornblith criticized popular arguments by Amos Tversky and Daniel Kahneman that intuition is irrational. He continued to argue that traditional induction explains the success of modern science.

Our [universal] conceptual and inferential tendencies jointly conspire, at least roughly, to carve nature at its [generic] joints and project the features of a kind which are essential to it. This preestablished harmony between the [generic] causal structure of the world and the [universal] conceptual and inferential structure of our minds produces reliable inductive inference.[4]: 94

## Hasok Chang and Rasmus Winther

Hasok Chang and Rasmus Winther contributed essays to a collection entitled Natural Kinds and Classification in Scientific Practice, published in 2016. The editor of the collection, Catherine Kendig, argued for a modern meaning of natural kinds, rejecting Aristotelian classifications of objects according to their "essences, laws, sameness relations, fundamental properties ... and how these map out the ontological space of the world." She thus dropped the traditional supposition that natural kinds exist permanently and independently of human reasoning. She collected original works examining results of discipline-specific classifications of kinds: "the empirical use of natural kinds and what I dub 'activities of natural kinding' and 'natural kinding practices'."[8]: 1–3  Her natural kinds include scientific disciplines themselves, each with its own methods of inquiry and classifications or taxonomies..

Chang's contribution displayed Kendig's "natural kinding activities" or "practice turn" by reporting classifications in the mature discipline of chemistry—a field renowned for examples of timeless natural kinds: "All water is H2O;" "All gold has atomic number 79."

He explicitly rejected Quine's basic assumption that natural kinds are real generic objects. "When I speak of a (natural) kind in this chapter, I am referring to a [universal] classificatory concept, rather than a collection of objects." His kinds result from humanity's continuous knowledge-seeking activities called science and philosophy. "Putting these notions more unambiguously in terms of concepts rather than objects, I maintain: if we hit upon some stable and effective classificatory concepts in our inquiry, we should cherish them (calling them 'natural kinds' would be one clear way of doing so), but without presuming that we have thereby found some eternal essences.[8]: 33–4

He also rejected the position taken by Bird and Tobin in our third quote above. "Alexander Bird and Emma Tobin’s succinct characterization of natural kinds is helpful here, as a foil: ‘to say that a kind is natural is to say that it corresponds to a grouping or ordering that does not depend on humans’. My view is precisely the opposite, to the extent that scientific inquiry does depend on humans."[8]: 42–3

For Chang, induction creates conditionally warranted kinds by "epistemic iteration"—refining classifications developmentally to reveal how constant conjunctions of relevant traits work: "fundamental classificatory concepts become refined and corrected through our practical scientific engagement with nature. Any considerable and lasting [instrumental] success of such engagement generates confidence in the classificatory concepts used in it, and invites us to consider them as 'natural'."[8]: 34

Among other examples, Chang reported the inductive iterative process by which chemists gradually redefined the kind "element." The original hypothesis was that anything that cannot be decomposed by fire or acids is an element. Learning that some chemical reactions are reversible led to the discovery of weight as a constant through reactions. And then it was discovered that some reactions involve definite and invariable weight ratios, refining understanding of constant traits. "Attempts to establish and explain the combining-weight regularities led to the development of the chemical atomic theory by John Dalton and others. ... Chemical elements were later redefined in terms of atomic number (the number of protons in the nucleus)."[8]: 38–9

Chang claimed his examples of classification practices in chemistry confirmed the fallacy of the traditional assumption that natural kinds exist as mind-independent reality. He attributed this belief more to imagining supernatural intervention in the world, than to illogical induction. He did not consider the popular belief that innate psychological capacities enable traditional induction to work. "Much natural-kind talk has been driven by an intuitive metaphysical essentialism that concerns itself with an objective [generic] order of nature whose [universal] knowledge could, ironically, only be obtained by a supernatural being. Let us renounce such an unnatural notion of natural kinds. Instead, natural kinds should be conceived as something we humans may succeed in inventing and improving through scientific practice."[8]: 44

Rasmus Winther's Contribution to Natural Kinds and Classification in Scientific Practice gave new meaning to natural objects and qualities in the nascent discipline of Geographic Information Science (GIS). This "inter-discipline" engages in discovering patterns in—and displaying spatial kinds of—data, using methods that make its results unique natural kinds. But it still creates kinds using induction to identify instrumental traits.

"Collecting and collating geographical data, building geographical data-bases, and engaging in spatial analysis, visualization, and map-making all require organizing, typologizing, and classifying geographic space, objects, relations, and processes. I focus on the use of natural kinds ..., showing how practices of making and using kinds are contextual, fallible, plural, and purposive. The rich family of kinds involved in these activities are here baptized mapping kinds."[8]: 197

He later identified sub-kinds of mapping kinds as "calibrating kinds," "feature kinds," and "object kinds" of "data model types."[8]: 202–3

Winther identified "inferential processes of abstraction and generalization" as methods used by GIS, and explained how they generate digital maps. He illustrated two kinds of inquiry procedures, with sub-procedures to organize data. They are reminiscent of Dewey's multiple steps in modern inductive and deductive inference.[8]: 205  Methods for transforming generic phenomena into kinds involve reducing complexity, amplifying, joining, and separating. Methods for selecting among generic kinds involves elimination, classification, and collapse of data. He argued that these methods for mapping kinds can be practiced in other disciplines, and briefly considered how they might harmonize three conflicting philosophical perspectives on natural kinds.

Some philosophers believe there can be a "pluralism" of kinds and classifications. They prefer to speak of "relevant" and "interesting" kinds rather than eternal "natural" kinds. They may be called social constructivists whose kinds are human products. Chang's conclusions that natural kinds are human-created and instrumentally useful would appear to put him in this group.

Other philosophers, including Quine, examine the role of kinds in scientific inference. Winther does not examine Quine's commitment to traditional induction generalizing from small samples of similar objects. But he does accept Quine's willingness to call human-identified kinds that work natural.

"Quine holds that kinds are "functionally relevant groupings in nature" whose recognition permits our inductions to "tend to come out right." That is, kinds ground fallible inductive inferences and predictions, so essential to scientific projects including those of GIS and cartography."[8]: 207

Finally, Winther identified a philosophical perspective seeking to reconstruct rather than reject belief in natural kinds. He placed Dewey in this group, ignoring Dewey's rejection of the traditional label in favor of "warranted assertions."

"Dewey resisted the standard view of natural kinds, inherited from the Greeks ... Instead, Dewey presents an analysis of kinds (and classes and universals) as fallible and context-specific hypotheses permitting us to address problematic situations effectively."[8]: 208  Winther concludes that classification practices used in Geographic Information Science are able to harmonize these conflicting philosophical perspectives on natural kinds.

"GIS and cartography suggest that kinds are simultaneously discovered [as pre-existing structures] and constructed [as human classifications]. Geographic features, processes, and objects are of course real. Yet we must structure them in our data models and, subsequently, select and transform them in our maps. Realism and (social) constructivism are hence not exclusive in this field."[8]: 209

## References

### Footnotes

1. Dewey, John (1938). Logic: The Theory of Inquiry. Holt, Rinehart, and Winston.
2. ^ Bird, Alexander; Tobin, Emma. "Natural Kinds". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy.
3. ^ a b Kornblith, Hilary (1993). Inductive Inference and Its Natural Ground. MIT Press.
4. Quine, Willard Van Orman (1970). "Natural Kinds". In Nicholas Rescher (ed.). Essays in Honor of Carl G. Hempel. D. Reidel.
5. ^ Hilary Putnam (1975/1985): "The meaning of 'meaning'" . In: Philosophical Papers. Vol. 2: Mind, Language and Reality. Cambridge University Press.
6. ^ a b Bird, Alexander; Tobin, Emma (2018), "Natural Kinds", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2018 ed.), Metaphysics Research Lab, Stanford University, retrieved 2019-11-23
7. ^ a b Putnam, Hilary (July 1970). "Is Semantics Possible?". Metaphilosophy. 1 (3): 187–201. doi:10.1111/j.1467-9973.1970.tb00602.x. ISSN 0026-1068.
8. Kendig, Catherine (2016). Natural Kinds and Classification in Scientific Practice. Routledge.

### Sources

• Andreasen, Robin O. 2005. The Meaning of 'Race': Folk Conceptions and the New Biology of Race. Journal of Philosophy 102(2): 94–106.
• Dupré, John. 2001. In Defence of Classification. Studies in History and Philosophy of Biological and Biomedical Sciences 32(2): 203–219.
• Gadamer, Hans-Georg. "Truth and Method". Continuum International Publishing Group, 2004. ISBN 082647697X, 9780826476975.
• Hacking, Ian. 1990. Natural Kinds. in Robert B. Barrett and Roger Gibson, F., editors. Perspectives on Quine. Cambridge, Massachusetts: Blackwell.
• Hacking, Ian. 1991. "A Tradition of Natural Kinds", Philosophical Studies, Vol. 61, No.1/2, (February 1991), pp. 109–126.
• Kendig, Catherine (ed.), Natural Kinds and Classification in Scientific Practice, Routledge, (Abingdon), 2016. ISBN 978-1-848-93540-2.
• Putnam, Hilary. 1975. The Meaning of 'Meaning'. in Keith Gunderson, editor. Minnesota Studies in the Philosophy of Science, vol. VII. Minneapolis: University of Minnesota Press.
• Willard Van Orman Quine (1970). "Natural Kinds" (PDF). In Nicholas Rescher; et al. (eds.). Essays in Honor of Carl G. Hempel. Dordrecht: D. Reidel. pp. 41–56. Reprinted in: Quine (1969), Ontological Relativity and Other Essays, Ch. 5, Columbia Univ. Press.
• Sokal, Robert R. 1974. Classification: Purposes, Principles, Progress, Prospects. Science 185(4157): 1115–1123.

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# Biotransformations of R-(+)-pulegone and menthofuran in vitro: Chemical basis for toxicity

Madyastha, KM and Raj, Paul C (1990) Biotransformations of R-(+)-pulegone and menthofuran in vitro: Chemical basis for toxicity. In: Biochemical and Biophysical Research Communications, 173 (3). pp. 1086-1092.

 PDF Biotransformations_of_R.pdf Restricted to Registered users only Download (274Kb) | Request a copy

## Abstract

Incubation of R-(+)-pulegone(I) with PB-induced rat liver microsomes in the presence of NADPH resulted in the formation of menthofuran(II) and 2′-Z-[2′-keto-4′-methylcyclohexylidene] propanol (III, 9-hydroxy pulegone) as the major and minor metabolites, respectively. When isopulegone(IV) was used as the substrate, the major metabolite formed was shown to have identical GC-MS fragmentation pattern to that of synthetic 2-[2′-keto-4′-methylcyclohexyl]prop-2-en-1-ol (V) and the minor metabolite was shown to be menthofuran (II). Transformation of menthofuran (II) by microsomes in the presence of NADPH yielded a metabolite identified as 2-Z-(2′-keto-4′-methyl cyclohexylidene) propanal (VI, pulegone-8-aldehyde). Formation of this $\alpha$ , $\beta$ - unsaturated aldehyde was further confirmed by trapping it as cinnoline derivative by adding semicarbazide to the assay medium. The toxicity mediated by pulegone is discussed in the light of these observations.

Item Type: Journal Article Copyright of this article belongs to Academic Press, Inc. Biotransformation;pulegone;menthofuran;metabolites Division of Chemical Sciences > Organic Chemistry 10 Dec 2007 19 Sep 2010 04:41 http://eprints.iisc.ernet.in/id/eprint/12471


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# How do you factor x^4 - 3x^2 - 4?

Apr 5, 2018

See a solution process below:

#### Explanation:

Because the ${x}^{4}$ coefficient is $1$ we know the coefficient for the ${x}^{2}$ terms in the factor will also be $1$:

$\left({x}^{2}\right) \left({x}^{2}\right)$

Because the constant is a negative and the coefficient for the $x$ term is a negative we know the sign for the constants in the factors will have one positive and one negative:

$\left({x}^{2} +\right) \left({x}^{2} -\right)$

Now we need to determine the factors which multiply to -4 and also add to -3:

$1 \times - 4 = - 4$; $1 - 4 = - 3$ <- this IS the factor

$\left({x}^{2} + 1\right) \left({x}^{2} - 4\right)$

The factor $\left({x}^{2} - 4\right)$ is a special form of the quadratic:

${\textcolor{red}{x}}^{2} - {\textcolor{b l u e}{y}}^{2} = \left(\textcolor{red}{x} + \textcolor{b l u e}{y}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{y}\right)$

We can factor this term as:

$\left({x}^{2} + 1\right) \left(\textcolor{red}{x} + \textcolor{b l u e}{2}\right) \left(\textcolor{red}{x} - \textcolor{b l u e}{2}\right)$


text:
# LocalTime arithmetic

In an attempt to calculate the time difference between two cities I enter:

LocalTime[Entity["City", {"Wheeling", "WestVirginia", "UnitedStates"}]] - LocalTime[Entity["City", {"LosAngeles", "California", "UnitedStates"}]]

The Output is

Quantity[-0.673196, "Seconds"]

This should be 3hrs

It's easy to find the numeric time offset in hours between two cities with TimeZoneOffset.

city1 = Entity["City", {"Wheeling", "WestVirginia", "UnitedStates"}];
city2 = Entity["City", {"LosAngeles", "California", "UnitedStates"}];
TimeZoneOffset[city1, city2]
(* 3. *)

Use Quantity to get the offset in hours.

Quantity[TimeZoneOffset[city1, city2], "Hours"]
(* Quantity[3., "Hours"] *)

Local time difference

Subtracting local times doesn't work is because the two times are the same time but in different time zones. The fractional second result happens because LocalTime for Los Angeles runs a short time after LocalTime for Wheeling. The difference is the fraction of a second that's needed to get the time for Wheeling.

Demonstrate that the two times are the same by using LocalTime to get the Los Angeles time for the current Wheeling time. The time in Wheeling is the same as the time in Los Angeles (only the time zones are different), so the difference is zero.

tWheeling = LocalTime[city1];
tLosAngeles = LocalTime[city2, tWheeling];
tWheeling - tLosAngeles
(* Quantity[0., "Seconds"] )*

• The documentation states that LocalTime[] returns a DateObject. If you extract the list using Part: LocalTime[ Entity["City", {"Wheeling", "WestVirginia", "UnitedStates"}]][[1]] you get {2020, 10, 22, 14, 59, 39.1685818} and for Los Angeles you get {2020, 10, 22, 12, 1, 22.4556520}. The format here is {y,m,d,h,min,sec}. Notice the difference in the h slot. When you subtract the lists you get the actual time difference contained in the resulting list. Just seems awkward to me that the times would internally be treated the same. I should dust my relativity text and review simultaneity.
– JEM
Oct 22 '20 at 19:07
• When you use part, you ignore the time zone information. The local times, with the time zones, are the same instant in time so the time difference is zero. The numeric values for hours, minutes and seconds, etc., are different, but that's because the time zones are different. If we convert Wheeling time and Los Angles time to a common time zone (GMT for example), we would see that all the numeric values are the same. Oct 22 '20 at 20:11

You could try LocalTimeZone like so:

LocalTimeZone[
Entity["City", {"Wheeling", "WestVirginia", "UnitedStates"}], Now,
"Offset"] -
LocalTimeZone[
Entity["City", {"LosAngeles", "California", "UnitedStates"}], Now,
"Offset"]
(* Quantity[MixedMagnitude[{3, 0, 0}],
MixedUnit[{"Hours", "Minutes", "Seconds"}]] *)


text:
Chapter Sequences and Series Review
Chapter
Chapter 7
Section
Chapter Sequences and Series Review
Solutions 65 Videos

Represent the sequence 2, 8, 14, 20, ... in words

0.44mins
Q1a

Represent the sequence 2, 8, 14, 20, ... algebraically

0.23mins
Q1b

Represent the sequence 2, 8, 14, 20, ... graphically

0.51mins
Q1c

How can you determine whether a sequence is arithmetic?

0.26mins
Q2

For each arithmetic sequence, state

• i) the general term
• ii) the recursive formula

58, 73, 88, ...

0.59mins
Q3a

For each arithmetic sequence, state

• i) the general term
• ii) the recursive formula

-49, -40, -31, ...

1.01mins
Q3b

Determine the 100th term of the arithmetic sequence with t_7 = 465 and t_{13} = 219.

1.36mins
Q4

A student planets a seed. After the seed sprouts, the student monitors the growth of the plant by measuring its height every week. The height after each of the first three weeks was 7 m, 20 mm and 33 mm, respectively. If this pattern of growth continues, in what week will the plant be more than 100 mm tall?

1.20mins
Q5

How can you determine whether a sequence is geometric?

0.35mins
Q6
• i) Determine whether each sequence is arithmetic, geometric, or neither.
• ii) Determine whether each sequence is arithmetic, geometric, or neither.

5, 15, 45, ...

0.38mins
Q7a
• i) Determine whether each sequence is arithmetic, geometric, or neither.
• ii) Determine whether each sequence is arithmetic, geometric, or neither.

0, 3, 8, ...

0.14mins
Q7b
• i) Determine whether each sequence is arithmetic, geometric, or neither.
• ii) Determine whether each sequence is arithmetic, geometric, or neither.

288, 14.4, 0.72, ...

0.55mins
Q7c
• i) Determine whether each sequence is arithmetic, geometric, or neither.
• ii) Determine whether each sequence is arithmetic, geometric, or neither.

410, 50, 90, ...$ Buy to View 0.35mins Q7d • i) Determine whether each sequence is arithmetic, geometric, or neither. • ii) Determine whether each sequence is arithmetic, geometric, or neither. 19, 10, 1, ... Buy to View 0.22mins Q7e • i) Determine whether each sequence is arithmetic, geometric, or neither. • ii) Determine whether each sequence is arithmetic, geometric, or neither. 512, 384, 288, ... Buy to View 0.48mins Q7f For each geometric sequence, determine • i) the recursive formula • ii) the general term • iii) the first five terms The first term is 7 and the common riot is -3 Buy to View 0.50mins Q8a For each geometric sequence, determine • i) the recursive formula • ii) the general term • iii) the first five terms a =12 and r = \frac{1}{2} Buy to View 0.43mins Q8b For each geometric sequence, determine • i) the recursive formula • ii) the general term • iii) the first five terms the second term is 36 and the third term is 144 Buy to View 1.28mins Q8c • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}. • ii) State the first five terms. t_n = 4n + 5 Buy to View 0.46mins Q9a • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}. • ii) State the first five terms. t_n = \frac{1}{7n -3} Buy to View 0.58mins Q9b • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}. • ii) State the first five terms. t_n = n^2 -1 Buy to View 0.41mins Q9c • i) Determine the type of each sequence (arithmetic, geometric, or neither), where n \in \mathbb{N}. • ii) State the first five terms. t_1 = -17, t_n =t_{n - 1} + n - 1, where n >1 Buy to View 1.03mins Q9d In a laboratory experiment, the count of a certain bacteria doubles every hour. a) At 1pm, there were 23000 bacteria present. How many bacteria will be present at midnight? b) Can this model be sued to determine the bacterial population at any time? Explain. Buy to View 1.30mins Q10 Guy purchased a rare stamp for \$820 in 2001. If the value of the stamp increases by 10\% per year, how much will the stamp be worth in 2010?

0.57mins
Q11

Toothpicks are used to make a sequence of stacked squares as shown. Determine a rule for calculating t_n, the number of toothpicks needed for a stack of squares n high. Explain your reasoning.

4.01mins
Q12

Determine the 100th term of the sequence

 \displaystyle \frac{1}{2}, \frac{2}{5}, \frac{3}{8}, \frac{4}{11}, ...

1.00mins
Q13

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle 1 + 9 + 17 + ...

0.51mins
Q14a

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle 21 + 17 + 13 + ...

1.02mins
Q14b

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle 31 + 52 + 73 + ...

0.57mins
Q14c

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle -9 - 14 - 19 - ...

0.29mins
Q14d

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle 17.5 + 18.9 + 20.3 + ...

0.36mins
Q14e

For each arithmetic series, calculate the sum of the first 50 terms.

 \displaystyle 39 -31 - 23 ...

0.36mins
Q14f

Determine the sum of the first 25 terms of an arithmetic series in which

the first term is 24 and the common difference is 11

0.30mins
Q15a

Determine the sum of the first 25 terms of an arithmetic series in which

t_1 =91 and t_{25} = 374

1.09mins
Q15b

Determine the sum of the first 25 terms of an arithmetic series in which

t_1 = 84 and t_2 = 57

0.45mins
Q15c

Determine the sum of the first 25 terms of an arithmetic series in which

the third term is 42 and the terms decrease by 11

1.12mins
Q15d

Determine the sum of the first 25 terms of an arithmetic series in which

the 12th term is 19 and the terms decrease by 4

0.58mins
Q15e

Determine the sum of the first 25 terms of an arithmetic series in which

t_5 = 142 and t_{15} = 12

1.17mins
Q15f

Calculate the sum of each series.

1 + 13 + 25 + ... + 145

1.05mins
Q16a

Calculate the sum of each series.

9 + 42+75 + ...+ 4068

1.42mins
Q16b

Calculate the sum of each series.

123 + 118 + 113 + ... - 122

1.20mins
Q16c

A spacecraft leaves an orbiting space station to descend to the planet below. The spacecraft descends 64 m during the first second and then engages its reverse thrusters to slow down its descent. It travels 7 m less during each second afterward. If the spacecraft lands after 10 s, how far did it descent?

1.23mins
Q17

For each geometric series, calculate t_6 and S_6.

 \displaystyle 11 + 33 + 99 + ...

0.34mins
Q18a

For each geometric series, calculate t_6 and S_6.

 \displaystyle 0.111 111 + 1. 111 111 + 11. 111111 + ...

1.29mins
Q18b

For each geometric series, calculate t_6 and S_6.

 \displaystyle 6 - 12 + 24 - ...

0.57mins
Q18c

For each geometric series, calculate t_6 and S_6.

 \displaystyle 11 + 33 + 99 + ...

1.23mins
Q18d

For each geometric series, calculate t_6 and S_6.

 \displaystyle 17 - 25.5 + 38.25 - ...

1.24mins
Q18e

For each geometric series, calculate t_6 and S_6.

 \displaystyle \frac{1}{2} + \frac{3}{10} + \frac{9}{50} + ...

1.28mins
Q18f

Determine the sum of the first eight terms of the geometric series in which

the first term is -6 and the common ratio is 4

0.22mins
Q19a

Determine the sum of the first eight terms of the geometric series in which

t_1 = 42 and t_9 = 2112

1.27mins
Q19b

Determine the sum of the first eight terms of the geometric series in which

the first term is 320 and the second terms is 80

1.06mins
Q19c

Determine the sum of the first eight terms of the geometric series in which

the third term is 35 and the terms increase by a factor of 5

1.05mins
Q19d

A catering company has 15 customer orders during its first month. for each month afterward, the company has double the number of orders than the previous month . How many orders in total did the company fill at the end of its first year?

0.41mins
Q20

The 1st, 5th, and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometrid sequence.

2.58mins
Q21

Calculate the sum of each series.

 \displaystyle 7 + 14 + 28 + ... + 3584

1.08mins
Q22a

Calculate the sum of each series.

 \displaystyle -3 -6 -12 -24 - ... - 768

1.32mins
Q22b

Calculate the sum of each series.

 \displaystyle 1 + \frac{5}{2} + \frac{25}{4} + ... + \frac{15625}{64}

1.04mins
Q22c

Calculate the sum of each series.

 \displaystyle 96 000 - 48000 + 24 000 - ... + 375

2.12mins
Q22d

Calculate the sum of each series.

 \displaystyle 1000 + 1000(1.06) +1000(1.06)^2 + ... + 1000(1.06)^{12}

0.50mins
Q22e

Expand and simplify.

(a + 6)^4

1.00mins
Q23a

Expand and simplify.

(b-3)^5

0.53mins
Q23b

Expand and simplify.

(2c+ 5)^3

1.04mins
Q23c

Expand and simplify.

\displaystyle (4 - 3d)^6

1.46mins
Q23d

Expand and simplify.

\displaystyle (3f^2-\frac{2}{f})^4

(3f^2 - \frac{2}{f})^4


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