Minimax Principle and Secondary Long-Term English Learners

by Natalia Heckman

If you are an ESL teacher, you have probably heard about Stephen Krashen. If you are an administrator, you have probably heard about John Hattie. If you have ever attended a campus accountability meeting, you must be familiar with the phenomenon of language stagnation. So what do Krashen, Hattie, and language stagnation have in common? They are connected through the principle of MINIMAX (maximum return on minimum investment).

Characteristics of Long-term ELs 

Students whose language journeys seem to freeze in time (fossilize) are often referred to as long-term English learners (LTELs). These students seem to pass the midpoint (Upper Intermediate or Advanced) and then hit their language breaks. Hard. As in, “I am not moving any further no matter what you do” hard. Years go by, and they are still at the same level, puzzling teachers, admins, and the entire ESL language community. 

The phenomenon of LTELs is so widespread that you can’t help but wonder if language stagnation is the natural course of events. Oddly enough, it seems to be the case if you consider research on language, brain function, and motivation.

We puzzle over this phenomenon. We gripe about unrealistic expectations of language proficiency tests (ACCESS, TELPAS, etc.), ponder over differences between social and academic language, and point out socioeconomic factors that appear to be common denominators.

Teachers say, “I would take newcomers over long-term ELs any day of the week because I can ‘move’ them much faster.” And quite frequently this is true! Grit propels newcomers forward with unfathomable force, and in two to three years, they leave the LTELs in the dust. Watching the formidable success of our newcomers, we wonder why our homegrown ELs can’t be more like them. And whose fault is it, anyway? 

Long-term ELs and Motivation

When it comes to language stagnation, all of the factors I mentioned are at play, but dwindling motivation seems to be the main culprit.

Krashen states that language acquisition is driven by different types of motivation, including integrative and instrumental motivation. 

Integrative Motivation is our desire to be like valued members of the community that speak the second language. We want to speak the language to fit in socially. “The integrated acquirer fossilizes or ceases progress when he perceives that his social needs are met” (Krashen, 1981, p.39).

Instrumental Motivation is marked by the desire to achieve proficiency for utilitarian or practical reasons. “The instrumental acquirer fossilizes or ceases progress when he perceives that communicative needs are met” (Krashen, 1981, p.39). 

Does this mean that motivation has a shelf life? Is there a critical period for motivation to acquire high levels in a second language? Can motivation be extended beyond its natural lifespan?

What does it look like for long-term ELs?

I have spent ten years as a classroom teacher on a secondary campus working with newcomers and long-term ELs, and I had plenty of opportunities to notice the differences between these groups. These are my empirical observations. 

Integrative Motivation 

Adolescent long-term ELs who have been in US schools since middle school or even elementary are socially comfortable, and their accents are indistinguishable from native speakers’. Being more proficient in English than any other language, they often claim it as their first language, and most importantly, they have no trouble fitting in; hence, the lack of integrative motivation. (Even if it did exist at first, it evaporated as soon as the social needs were met.)

Instrumental Motivation

Many students have jobs that allow them to make a decent paycheck. The language they have developed by that point (the lower region of Advanced) is enough; therefore, the instrumental motivation has subsided and eventually ceased to exist. My kids told me, “Miss, don’t worry. My English is fine. Next year, when I graduate, I will be making more money than you working as a pipe fitter at a chemical plant. Why do I need to worry about TELPAS?” (TELPAS is the language proficiency test the kids take in Texas.)

As a result, it is usually easier to move a newcomer from Beginner to Advanced High in the first two years in the US schools (while language is still perceived as vital) than to have an LTEL progress from Intermediate to Advanced or from Advanced to Advanced High after being in the country for five or six years. It seems there is a stagnation point beyond which it is rather difficult to regain language momentum. 

So, now what? 

Students’ motivation is directly related to and regulated by unconscious psychological responses to the smallest changes in their reality. 

In language learning, many processes cannot be controlled consciously, and they happen as they happen when they happen as a response to our reality. In other words, language development is correlated with our perception of its ability to satisfy the need for communication. No need, no language. 

MINIMAX: Are low expectations contributing to language fossilization? 

Here comes the MINIMAX principle. 

Hattie says, “Their [students’] expectations are so often based on the ‘doing just enough’, or the minimax, principle—that is, maximum grade return for minimum extra effort” (p. 83).

Inadvertently, schools might be promoting an environment where motivation is not only not  being fostered, but where it can actually be lulled to sleep by low expectations. 

To work harder, you need a fire under your tail, and the moment that fire is put out, your brain stops trying. 

What conditions can put out that fire? In a classroom, it may look like this: “Why should I read the textbook if I can pass a quiz with a 70 after listening to the teacher talk me through the slides in class?” There is nothing wrong with learning through a lecture, but you do not develop high-level academic reading/writing performance without reading those heavy academic texts from a book that weighs a ton. But if you can pass a quiz with a 70 without any reading at all, why would you bother? 

Now, let’s go back to Krashen: “Instrumentally motivated students may acquire just those aspects of the target language that are necessary” (p.22). Grasping a basic idea from a lecture and being able to pick the right answer on the multiple choice test does not require Advanced High levels of speaking, listening, reading, or writing. 

By allowing students to get by on the MINIMAX principle, we not only assure them that minimum investment of effort is a safe route, but we also promote the fossilization of the language. 

What does brain research say? 

The ultimate goal of our brain is to keep the body alive at a minimum caloric cost. The brain is constantly looking for shortcuts to save calories and tuck them away for later. As a result, it requires an immense amount of energy (the type that our brain is trying to preserve) to will yourself into taking a more challenging pathway, especially if the immediate goal can be achieved at a lesser cost. In other words, you might find it impossible to bring yourself to read the textbook knowing that you can get that 70 without spending precious “calories” on reading. 

What can educators do to offset lacking motivation? 

Surpassing the basic level of language development is not easy. Neither is it effortless. Continuously gaining one level of progress per year is not guaranteed. In fact, it gets progressively more and more difficult to sustain the upward momentum the higher you get—the closer to the top, the steeper the climb. And, once you camp out at a comfortable level for some time, you are probably not going anywhere unless a sudden spark of motivation restarts your engine. 

So, what can teachers do? Hattie (2012) says we can “create new horizons” and combat complacency by making it more difficult for students to get by on MINIMAX. 

“Students so often set ‘safe’ predictions, and our role as educators is to raise these student expectations. Our role is not to enable students to reach their potential, or to meet their needs; our role is to find out what students can do, and make them exceed their potential and needs. Our role is to create new horizons of success and then to help students to attain them” (p.83). 

It appears more feasible to catch the students before the fossilization sets in rather than trying to reverse the process. It’s really hard to undo language stagnation, so preemptively addressing the challenge might be the better course of action. Here are some ideas: 

Apply M.A.Q to transform the way your students experience language instruction

As teachers, we can control the reality in our classrooms! Foreign language expert Anna Matis uses M.A.Q. to sustain and promote students’ language development. 

  • Motivation 
  • Access to Language
  • Quality of Instruction

Read the blog post where Anna explains how she uses M.A.Q. “to effectively scaffold my instruction and create access points to the target language for various groups of my learners” (Matis, 2018, p.19).

Recommend ELs for Dual Credit, Pre-AP, and AP courses 

Rigor is necessary to challenge and stretch students’ abilities. Finding pride in accomplishing academic goals boosts and extends the shelf life of motivation. Do not think that the class that requires significant reading is not the right fit for your ELs. Quite the opposite! Watch this video of Dr. Carol Salva’s student talking about taking a PreAP ELA class. These classes are especially beneficial for students who have high literacy in their first language, since many reading skills beyond fundamentals do transfer to the second language.

Foster a love for reading through classroom libraries and SSR. 

The amount of reading students do is the best predictor of language growth. The primary goal of a classroom library is not to have kids read in class every day but to plant the seed of literacy and extend love for reading well beyond the walls of your classroom. SSR alone is not enough, but when a student asks to take the book home after reading for 10 mins, it’s a job well done on our part! 

(David Goodwin (2002) @ThinkReadTweet) 

Invite motivational speakers.

Meeting people who have not settled for less than their potential is empowering! Meeting successful community members and people with similar backgrounds helps students set lofty goals that require extra effort. See Dr. Salva’s padlet, and listen to her podcast on mindset and goal setting! 

Promote joyful learning! 

I admire Dr. Carol Salva for sharing resources on relevant, engaging, and compelling lessons. I wrote a blog about joy and engagement a while back, inspired by her message. We cannot simply drill our students towards higher proficiency, but we can create lessons that are relevant and joyful and that allow students to experience bursts of success! See more lesson ideas in my blog.  

Want more insights from Natalia?

You’re Invited to a Book Launch!

Building Better Writers, by Natalia Heckman

Created with emergent bilinguals in mind, Building Better Writers and the workshop attached to it aim to offer an asset-based perspective on writing instruction for newcomers in a self-contained ESL/ELD classroom and long-term ELs enrolled in mainstream ELA courses. Many parts of this resource, especially the chapter on composition, address specific skills that students will need to shine on the mandatory state end-of-course examinations. 


Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge.

Heckman, N.(2021). Joy of learning: Engaging students in every classroom. Secondary English learners.

Krashen, S. (1981). Second language acquisition and second language learning. Pergamon Institute of English.

Sharriton, T. (2022, May 5). Five ways to: Weave reading into curriculum. Teacherhead.

Matis, A (2019) How M.A.Q changed my life. Seidlitz Education.

Matis, A. (2018). Seven steps to a language-rich, interactive foreign language classroom. Seidlitz Education.

Salva, C. (2017, January 6). Gerson Dec 2016. 3rd year in US schools [Video]. Youtube.

Salva, C. (2017, June 22). How he went from beginner to Adv High in reading in 6 months [Video]. Youtube.

Salva, C. (2022). Back to school mindset and resources: The boosting achievement ESL podcast. Newcomers at Grade Level and Beyond.
Salva, C. (n.d.). Success for SLIFE

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