Archive for the ‘Formative Assessmnt’ Category

Formative Assessment Practices of a Teacher of Occupation-related Basic Math in an Integrated Education Program

December 22, 2017

This is a lightly edited excerpt from Teaching, Learning and Assessment for Adults Improving Foundational Skills, by David J. Rosen and Inge De Meyer, case studies in formative assessment in adult basic skills education in Belgium, published by OECD.[1] It is a description of an adult basic skills math teacher who teaches in a math lab, and who focuses on occupation-related math skills, using formative assessment and a learner-centered, blended learning model that incorporates some online instruction.

Formative assessment practices

The most important player in this case study is the mathematics teacher from the center for adult basic education who is out-stationed in the public employment service (VDAB). She uses several formative assessment practices to address the specific educational needs of each of her students and to help them acquire the skills they lack for their future job. Furthermore she keeps every party involved in this project informed about the participant’s progress and problems. Without such a dynamic, communicative math teacher with experience in teaching adults with basic skill needs, the program wouldn’t be as successful.

Formative assessment practices the teacher uses include:

  • Formative assessment. For each learner, the teacher assesses which of the skills needed to follow their chosen vocational training they lack, and she works with each individually towards acquiring those skills. During this process she doesn’t use the general summative approach used in basic mathematics courses. Instead, learning and assessment are carried out through individual tasks, which she discusses with the learners. This personal, informal feedback helps the learners to clarify their knowledge and proficiency level without formal testing.
  • Dialogue with the learners (individual conversations during which the individual learner’s problems are discussed). During these individual conversations she sometimes refers to other learners in the group to encourage the person she’s working with (“He/she also learned to do this. Was it very difficult to learn?”).
  • Peer learning. When learners in the math class are following the same (or a similar) vocational course and have similar mathematical needs the teacher gives them tasks they can work on together.
  • Teacher “log” – for each learner the teacher notes the learner’s progress and his/her further needs so she can adapt the tasks in the next class to each learner’s actual numeracy level.
  • Learner progress communication – in writing  – with the learner, vocational teacher (VDAB instructor) and VDAB counselor. This way everybody involved in the program can take the problems and progress for each learner into account in the activities within the individual trajectories for which they are responsible.


When we observed experienced, out-stationed mathematics teacher Heidi D’Haene working with learners at the VDAB, there were two brightly-lit rooms, one with tables where learners worked independently, and a small computer lab. On one of the tables were neatly arranged binders and resource materials for the afternoon’s learning. The binders included, for example, math for builders, metal workers, plumbers and electricians, and vocationally-specific math assessments. The materials included an original copy of each competency-based instructional module or exercise, copies that the learner could write on and keep, and an answer sheet that the learner could use to correct her or his work.

Learners in the vocational courses at the VDAB found their way to the open mathematics lab in different ways. Their vocational teachers referred some to improve specific math skills that needed to be strengthened. Some were referred after having taken a math diagnostic test as part of their seeking a vocational course, for example as plumbers, electricians, builders, or metal workers. Others found on their own that they needed to strengthen certain math skills or, placed on a job, found a work task that required better facility with certain math skills.

Typically learners come to the math lab once a week, for two hours in the afternoon, for as many weeks as they need to accomplish their goals. Most learners finish their trajectory in around three months, after approximately 30 hours of instruction. On the day we observed there were six learners, all men aged 18-25.

In our interview with Heidi we learned that her primary interest is to help learners think in math and process it – not just learn the math facts and algorithms. She said that over time she has learners in the lab who have a very wide range of abilities, and her challenge is to be able to quickly and effectively adapt to that range, to their individual needs and goals. She explained that when possible she groups learners with the same goals who are at the same level, or she uses peer-learning methods. However, since this is not always possible, she always has materials for individually-paced learning related to each learner’s goals. Furthermore she doesn’t always know in advance who will be in the open lab for a given session, and she may have only one or two learners one day, and up to 15 on another. This makes adapting to learners’ needs challenging.

When learners begin in the open lab they often plan to attend up to 10-12 times, but they have the option of attending up to 30 hours before they are placed in a job. Occasionally a learner who is placed on a job comes back to work on a particular math task. A new learner may take (the relevant parts of) a mathematics diagnostic assessment, although sometimes there isn’t time for this. Heidi also experienced that several learners find taking a test difficult; they fear that it’s “like school.” Many of the learners, she said, rely on formulas and “tricks” to do math and have no real understanding of how to think mathematically. So she relies on direct, systematic observation of their learning as they try specific math tasks. For example, she hands a learner a worksheet and says, “Try this out. It may be too easy or too difficult. We’ll see.” Afterwards she closely observes how they are doing and adjusts the kind and level of instruction accordingly.

Using computers is integrated into the instruction, usually for 15 minutes at a time. Learners use educational software from a CD-ROM or from a web page. Heidi observes what they are doing, and together she and the learner assess whether they are ready to go on. She does not use learning management tools such as those that might be found in large integrated learning system software. She prefers direct talking with learners and poses questions such as “What do you want to learn here in the lab?” “Have you seen this (module, computer instruction program, etc.) before?” “Does it look like something you can do?” “Does this look like what you need to learn in order to…?”. She considers dialogue an important part of the formative assessment process; “it captures their motivation”.

Heidi tries to incorporate project-based learning whenever possible. This way the mathematics skills are grounded in situations that the learners find vocationally relevant. One of the projects Heidi described is making a plan of a garden house. This can be done as a team or as an independent project. It involves linear and area measurement, reading the instructions for and mixing cement, planning a budget and other numeracy or mathematics, reading and writing skills.

When there are only a few learners this method of working is not difficult. However, when there are more learners, she must move quickly through the lab, and back and forth between the two rooms to stay in touch with how each learner is doing and assign new work – a model sometimes referred to as “teaching on roller skates.” It requires a high degree of expertise in mathematics knowledge, teaching strategies, and the ability to mentally keep track of how each learner is doing.

Immediately after each session Heidi takes careful notes on what each learner has accomplished and what the learner needs to do next time. She discusses her notes with the learner at the beginning of the following open math lab session. She also sends a copy of the progress notes, immediately after the session, to the VDAB instructor who teaches the vocational course the learner attends and to the learner’s counselor at the VDAB. This communication accomplishes several things. First, it keeps the VDAB instructor and counselor informed of the learner’s progress. Second, it builds and maintains good relationships between the job skills training, VDAB counseling and basic skills staff.

Heidi also sometimes suggests ways in which, in the vocational classes, the numeracy skills could be reinforced. Collaboration with the professional VDAB training instructors is also practiced as new assessments are developed. Heidi works one-on-one with the vocational instructor to assess the numeracy skills and knowledge needed for training and for the job. In some cases this includes understanding math theory as, for example, understanding the binary system is important for certain kinds of electrical work. Heidi also works with the VDAB vocational instructors to tailor the curriculum to the needs of the vocational training, and the needs of the learners. For example, often a curriculum needs to have more levels added to address a wider range of learner needs.

This case is an excellent example of a multiple-partner, work-based, formative assessment model where all the elements are in place for participant success: a strong education and training skills agency partnership, an experienced and effective teacher, a well-developed competency-based curriculum that is related to participants’ goals, a well-developed formative assessment process, and basic skills learning embedded or contextualized in the highly-motivating training context.

[1] Rosen, D.J. and I. De Meyer (2008), “Case Study: Belgium (Flemish Community)”, in Teaching, Learning and Assessment for Adults: Improving Foundation Skills, OECD Publishing. 2008 Last downloaded December 22, 2017.