Language learners acquire grammatical structures in a predictable, natural order, independent of the order in which they are taught. — Dr. Stephen Krashen

The Natural Order Hypothesis states that there is an internal sequence that the brain tends to follow when building up the grammar of a new language. Some grammatical “chunks” or vocabulary groups are easier and emerge earlier, while others come only later, even if you explicitly study them first.

For example:

• English learners typically acquire –ing (progressive) before 3rd person –s (he runs), no matter their first language or the teaching sequence.

• This pattern is seen even if you teach “he runs” early — learners will still make errors like “he run” until their internal system is ready.

The point of the NOH is extremely simple. We want to be better learners and better teachers, so some guidelines on what to teach first would be greatly appreciated! We don’t want to waste our time teaching vocabulary and grammar that the students simply cannot learn, or face significant headwinds to learn, versus what they are naturally ready to learn now.

Examples of Natural Order

As stated above, progressive -ing is accquired before third person -s. We know other things about the natural order too, thanks to the work done by Dr. Stephen Krashen and linguistic scientists all over the world who have reproduced his NOH experiments and verified the results.

Input Hypothesis

Input Hypothesis is the N+1 idea and it connects directly to the Natural Order idea. N represents what you can already understand. +1 is the next small step in the natural order — the next grammatical or lexical item your brain is ready to pick up. So, comprehensible input works best when it’s just a little above your current level, containing features that are the next step in the natural order.

In short:

Natural Order gives the “map”; i+1 gives the “step.”

This is the clue we need to reverse-engineer the natural order.

Simple Weights and Measures

By the use of fair and simple weights and measures, we can constrain a score to match a word’s natural order. The first essential weight is anything which determines what a student already knows or doesn’t know. This is a picture of N. With a significant amount of data, we should be able to construct a bell curve that implies a progression through N to N+1 to N+X. For example, a flashcard quiz is given. The cards which are ‘known’ by an intermediate student should have a high probability of being ‘known’ by another intermediate student. That is, the words they know are not random, but very similar. There will be some words one student knows that another student doesn’t know, but for the most part, if one intermediate student knows a word, it can be considered part of N.

Differential N is also a way to get to N+1. Given the above observation about intermediate students, Considering Student 1 and Student 2, if S1N > S2N, then “+1” is likely to be found in S1N-S2N. That is, the words that S1 knows that S2 doesn’t know, are highly likely to be close to the +1 that Student 2 needs to satisfy N+1. This is because if S1 is more advanced than S2, it is likely because he has better studied the material he is being tested on. Therefore, if we can establish a standard ‘known’ vocabulary for a certain level, and establish also what words they don’t know, it is then possible to look at all of the intermediate words that some of them know and some of them don’t and place them into three bands:

• A) Known by approx. 90% of intermediate students
• B) Known by 10%-20% of intermediate students
• C) Unknown in general

In this example, N is represented by A) and +1 is represented by B). These lists of words can be discovered by experimental data. Below I will list some of the data I am using to construct the NOGL scores.

But first let’s discuss how NOGL is constructed.

Intial Scores

Intially, each word in the dictionary is given a unique integer number at random. This is it’s initial NOGL score. It is also given a NOGLC which is the confidence rating of that score.

Word Comparison Tool

The first method of weighting the scores is the Word Comparison Tool (WCT). The WCT presents two random words and asks the operator (who must be a native speaker) which word is easiest. It then exchanges the NOGL scores if they chose the word with the higher NOGL score. It also increases the NOGLC of each word by 1, whether an action was performed or not. It then chooses the next two words from among the words with the lowest NOGLC scores.

The noglc increases when:

• two words are chosen and their order is confirmed as correct by the native speaker operator.
• two words are chosen and their order is confirmed by the native speaker and changed in the database.

From this test, then, the noglc represents the number of times a native speaker has confirmed the ease of a word.

Automated by CEFR and Frequency

Although things like CEFR and word frequency do not necessarily imply natural order, it is highly unlikely that an A1 word should have a higher NOGL score than a C1 or C2 word. Therefore, although it is not directly intended that the NOGL will align with CEFR in the end, automatically processing over CEFR is a good way to push the list “towards” what a human would do, and then let a human clean up the mess left by CEFR. Therefore several automatic iterations were performed using the WCT but automated via comparing the word’s CEFR score.

Automated by Game and Test Results

Between ten and twenty students in Taiwan were given the opportunity to play web-based interactive learning games such as memory with images and words, a spelling game with images and audio cues, and a flashcard game where audio and a word is displayed and they must choose the correct card (i.e. multiple choice). Students usually preferred to play the multiple choice flashcard game because all they had to do was listen to the audio and read the word and click on an image. While not perfect, it is a rough estimate of what a particular student knows.

As the games were played, each time a student got a wrong answer, that word would be increased by 1 point. And, words were shown initially lowest scores first. This is a little like the WCT; two to four words are shown, if the word is easy it’s score remains low, but the words that typically cause students to fail go up and are not shown until later difficulties. This is a slow way of organizing words by what may appear to be natural order.

Across four different games and the WCT overseen by several foreigners, scores began to emerge. Initially it was mostly replacements. For example,

• hope had a score of 10122 and was exchanged with contributor’s 1997.
• pain had a score of 5862 and was exchanged with conscience which had a score of 1911.
• other exchanges observed were authentic vs. mail, taste vs. inadequate, and and goldfish vs chaos.

Over time as the NOGLC increased, words began to sort into a semblance of order. Here is a comparison of the words with NOGL scores 100, 1000, 2000, 3000 and 6000:

• 100. Color
• 1000. Cat
• 2000. Bullet
• 3000. Eminently
• 6000. Needlepoint

Although not perfect, it does seem that the words are roughly ordered. Consider that there are 10,000 words in the dictionary and if organized into even groups, an A1 rating (1st out of 6) would represent the first 1500 words. So while you may argue that ‘Cat’ should appear earlier than ‘Color’, they are already close in terms of banding. And, this is only with a NOGLC of between 2 and 3 from random scores. As NOGLC approaches (perhaps, 10) and data is added from the tests and games, we expect the NOGL score to improve over time.

Manual Editing

With 10,000 words in the dictionary, it is possible that a word just has a bad day. If the easiest word in the world had the most difficult score, and was compared against others randomly 10 times, it is very likely it would end up with a NOGL score close to, but still significantly different from where it should be. This will be reflected in it’s NOGLC score. We don’t know what a good NOGLC score would be. The comparisons are random (but consider noglc) so without manual editing it may be very difficult to get a correct score even with a noglc > 10.

The solution is manual editing. The operator simply looks at the list and chooses a word that seems drastically out of place. The operator then places that word where he thinks it belongs. This is a more advanced process since every other word needs to move its nogl score up (or down) by 1 to accomodate the move. Or, use the BASIC principle; increase scores by times-ten, and just insert the new words wherever you want and re-order later. NOGL is relative; it can be calculated from the existing list if needed. Otherwise there is no need to remember a nogl score; only it’s relative score.

Hmm! Let’s try that. nogl scores will be x10 and in practice we will just drop the last digit. Lets call the last digit a decimal! Oh, that is interesting.

In any case, the purpose of NOGL is to discover the natural order.

Ultimately, if it replicates the mental learning curve demonstrated by actual students, then it must be useful in replicating that mental curve when teaching English. By using these weights and other similar, simple and fair weights, we believe that NOGL will come to approimate the natural order, becoming more and more accurate over time.