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In my lessons I work intensively with the learning market. In subjects such as math, up to 90% of the lesson time is devoted to the use of this method. Depending on the author there are a variety of definitions that highlight the differences between the learning market, learning stations, weekly-plan based learning and project-based learning.

To begin, I teach two to three regular math lessons in which I indtroduce the topic. For example, fractions are introduced with a small game (I share three licorish rolls between four people etc.) Small excerises on the topic of fractions are done to illustrate the fact that ½ is the same as 2/4. These first few lessons barely scratch the surface of the topic. Some student understand, but but for many it goes in one ear and out the other. This introduction should, however, be just that…an introduction.

imageThe real learning happens in the second phase and centers around the initial example. Over the course of three to four weeks we enter the workshop/activity phase, in which the learning market strategy is employed. In this teaching strategy, individual math problems are printed on laminated flashcards. In most cases the solution is printed on the back of the card. The collection of flashcards will be placed at various locations in the classroon (e.g. some on the on the window sill etc.) Working independently, students can select any card of their choice and attempt to solve the problem. The unique aspect of this activity is the fact that flashcards are designed with differing levels of difficulty which allows both weaker students and those who are more advanced to work on problems appropriate for their level of understanding. The level of difficulty is indicated by the color of the flashcard. Green represents the most basic level , yellow indicates more challenging problems, and red indicates problems appropriate for only the most advanced learners.

As a teacher I now have the freedom to engage with the children—especially those who need more assistance than others. This avoids the situation in which more advanced learners are forced to waste time listening to repeated explanations of concepts they have already understood. Furthermore, each student can decide for him or herself whether or not he or she would like to try another basic problem or move on to the more challenging ones.

At the beginning of the learning market activity the children draw a chart in their notebooks like the one below:


In the table they record which level station they have already attained.

A corresponding chart is also hung in the classroom. If a certain student has understood a concept particularly well, his or her name can be recorded on the chart in the „expert“ column, as seen here:

1Rüdiger, Stefan
2Amelie, Jana

imageStudents who have questions can either ask me or their classmates who have achieved expert status. Additionally, there are „help charts“ on which the rules for calculation are explained and illustrated using examples. On each of the flachcards a small symbol is printed, indicating which help chart students may turn to if they face difficulties solving a problem. To illustrate, the symbol „H4“ indicates that instructions can be found on help chart number 4. This way, there are three different ways stundents can approach solving the problems.

For one or two weeks, the lesson is focused exclusively on these types of activities. Each student progresses at his or her own pace at the appropriate level of difficulty. This is followed by a phase of solidification that is gradually introduced. A mandatory „Station of the day“ is introduced which all students are required to complete and/or review. The solution to the station of the day is discussed in the last 10 minutes of class to ensure that all students have correctly solved the problems in their notebooks. In the final phase, another two or three lessons are devoted to systematic clarification, practice, and drills. The students are then tested on their knowledge and the process is repeated.

The learning market usually consists of 25 stations. To avoid the situaton in which students continually come to me to validate their answers, the solutions will be printed on the back of the flashcards. For this method to be successful it is paramount that the student do not betray themselves: Whoever only copies the solution into their notebooks without doing the work will not truly understand and retain the material. For this reason I do not check how many stations a student completes in a given lesson. This would only pressure them into copying solutions for the sake of meeting a required minimum number of problems and discourage true learning. I, therefore spend a significant amount of time emphasizing the fact the I will not be checking either the correctness of the answers of the number of problems they have solved. They must undertand that their own learning and performance is what is at stake and by cheating they will only be harming themselves.

The completion of green and yellow cards are mandatory for all students and all assessments contain problems and examples that were already introduced on the flashcards. This being the case, those who progress through the stations quickly gain the advantage of knowing which questions will be on the classwork assignment or quiz. This helps motivates the students to be both thorough and quick in working through the problems. At the same time, knowing that the same problems will be repeated on upcoming assessments reduces the anxiety children feel when faced with major math test.

imageThe red cards are most appreciated by the „stars“ of the class and serve as a buffer…keeping those who finish more quickly occupied in a meaningful way. These are often problems from a higher level class or exceedingly complicated examples. The educational concept of accomodation/support in the classroom focuses primarily on the weakest students in the class. Though helpful to student with learning differences, this approach makes keeping more advanced students engaged in the classroom extremely difficult. The „red card“ category of the learning market approach offers a solution to this problem. The most impressive aspect of the whole approach is the fact that it consistently keeps the level of student engagement at close to 100%. For students, the challenge of trying to master over twenty learning stations is far more motivting than the more traditional approach to teaching math, in which students are confronted with an endless array of worksheets or textbook-based drill excercises. The latter approach is by far more exhausting for students and easily becomes demotivating. The learning market method also has the added benefit of reducing the amount of frontal teaching required, allows me to give students individual attention, and even allows for periods of casual observation. All of these advantages ultimately benefit the students.

It can be said that, this does not represent the absolute best employment of the learning market method—at least according to university-level standards. After all, my method could potentially include other strategies such as „learning with the five senses“ or Bruners E-I-S principle. While such methods can add to the learning experience, it tends to be impractical for everyday use. (Consistently seeking ways to include elements that can be constructed, tasted or smelled is overly time consuming and not always well-suited to class content.) Nevertheless, I may consider including some of these elements as I revise and adapt class content over the course of the year.

The basic principal of the learning market is not only applicable to math, but can be easily adapted to the subject of physics as well. When dealing with Pythagoras only one or two problems are included on each flashcard, if calculating with fractions, a dozen. SuS handle this type of activity very well. They experience a sense of accomplishment when they complete and entire flashcard and aren’t confused or distracted by complicated explanations, info graphics, or pictures, as they are when using a textbook. You can find a more in depth discussion of textbook use here.

Evaluated on the basis of Hilbert Meyers ten criteria for good lessons, the method proves to be well-founded:

1. Clear lesson structure-
All students have a full understanding of the nature of the tasks with which they will be confronted and, on the basis of the progress summary chart in their notebook, know how much they have yet to achieve.

2. High percentage of true learning time –
On average about 44 minutes of the lesson are devoted to active learning, only a few minutes are devoted to greeting and introduction.

3. A classroom environment condusive to learning-
The „expert“ system, opportunities for one-on-one instruction time, and differentiated learning activites, students face few obstacles to learning.

4. Clarity in content –
Being that activities are designed to progress from the least to greatest level of difficulty, student have the opportunity to begin with the level of task they understand best. Color coding (green for low, yellow for intermediate, and red for advanced.) provide an easily recognizable indicator of the level of content.

5. Meaningful communication –
Varies from school to school based on scholl culture and clientelle

6. Diversity of teaching methods –

7. Student-specific teaching and differentiation-

8. Intelligent practice –

9. Clearly communicated standards / expectations –

10. Well-prepared learning space –

Now, after several years, my pupils leave school without ever having a regular school math-book. They learned everything in the learning market. Here you find a free template to create your own learning market – the template has proved its worth. To print an export in .pdf and then print two cards on an A4 page is recommended.

A few learning markets with free content you can find here. I’m working on being able to offer this material as open source here, but that’ll take some time.