The project is engaging with both educational institutions and enterprises in Finland, Romania and the United Kingdom. At the beginning of the MALog project a needs analysis was conducted to establish the mathematical logic requirements of students and companies.

Aspects of mathematical logic can be found in many universities and schools. We wanted to discover the types of material that is currently taught, the delivery mechanism and the problems encountered when learning about different types of mathematical logic. We also engaged with businesses who perceive a mathematical logic skills shortage within their organisation. The project wanted to discover how this manifests itself in the workplace and how educational materials can be designed and deployed to best address these issues.

The needs analysis consisted of surveys and interviews to identify mathematical topics encountered, the delivery mechanism and the types of problems encountered. An analysis of the results is helping the project to decide what kinds of material should be produced and how this material should be delivered.

Questionnaire and target group

A questionnaire was distributed to students in all the partner institutes with the aim of determining the main mathematical logic problems encountered. Representatives from companies were interviewed to ascertain their particular training requirements. As part of this process, real-life problems were identified.

The questionnaire for the students contained four different sections. The first section (questions 1-10) asked about the student and their educational background. The second section (questions 11-15) gathered data about mathematical logic and student’s current course. The third section (questions 16-19) included questions about their attitudes to teaching and learning and the last section (question 20) asked students about the contribution to learning of particular educational resources.

There were 360 responses to the needs analysis questionnaire from two upper secondary schools (Finland and Romania) and from three universities (Finland, Romania and England). Of these responses, 77% were male students and were 23% female students. The students were in the age bracket of 15-40 years with a mean of 20.6 years

Conclusions

You and your studies

Students were asked to identify whether they had previously studied mathematical logic. Over half (54%, 196 students) of the students had not studied mathematical logic previously (with the remaining 46%, 164 answering “yes"). Of the students who answered affirmatively, 47% of the students had spent less than 30 hours learning about mathematical logic, 30% for between 31 and 60 hours and the remainder for between 61 and over 150 hours. These results indicate a large percentage of students have spent little or no time studying the topic.

The majority of the respondents (83%) estimated their mathematical skills as Average/Good.

Mathematical logic and your current course

Truth tables were identified as the easiest topic of all those given in the questionnaire – 65 % of students labeled it ”very easy” or “easy”. Boolean algebra, propositional logic and set theory were rated more challenging. Topics such as predicate logic, proof and recursion theory were identified as more difficult topics with a greater number of students identifying the topics as ”difficult” or ”very difficult”.

In a follow-up question, students were asked to identify the reasons for their difficulties with particular topics – any that they had listed as ”difficult” or ”very difficult”. Several options were available for selection – ”material too difficult”, ”too much to learn”, ”learning materials not clear”, ”not explained well enough”, ”too weak background” or ”other”. We excluded students who have given a reason but not listed the topic as ”difficult” or ”very difficult” in the previous question.

• Truth tables – the two difficulties given were that material was not explained well enough and that background knowledge was too weak.
• Boolean algebra – the three difficulties given were that material was not explained well enough, material too difficult and too much to learn.
• Propositional logic – the four difficulties given were too much to learn, material too difficult, was not explained well enough and background knowledge was too weak.
• Set theory – the two difficulties given were too much to learn and material not explained well enough.
• Predicate logic – the two difficulties given were material too difficult and that background knowledge was too weak.
• Proof – the two difficulties given were material not explained well enough and material too difficult.
• Recursion theory – the two difficulties given were material too difficult and material not explained well enough.

In the next section of the questionnaire, students were asked about various aspects of teaching and learning mathematical logic. The first of these questions asked students to identify the difficulty of learning about mathematical logic in particular settings.

The respondents perceived the easiest way of learning issues in mathematical logic was by “Exercise/problem classes”, “Lectures/Classroom teaching” and “Working with the computer” and the most difficult way of learning was individual study with learning materials.

The next question asked students to rank in order the environments in which they spent the most time learning about mathematical logic. The following table presents these in rank order (from highest time spent to lowest time spent).

The respondents answered the question ”How easy do you find it is to learn mathematical logic material in a particular setting?” that the easiest ways of learning were ”Exercise/problem classes”, ”Lectures/Classroom teaching” and ”Working with the computer”. However, for the question ”Where do you spend the most time learning aspects of mathematical logic?” the respondents said they spend the most time for ”Lectures/classroom teaching” and ”Exercise/problem classes” and the least time for ”Working with the computer”. This would indicate that the students would like to learn mathematical logic with the help of a computer, but at the moment the teaching does not offer such an opportunity. Also the students found that the most difficult way of learning was individual study with learning materials.

Our project offers the solution to these problems by producing pedagogically high quality learning material units. This learning material will include ontology data, learning goals, prerequisites and different scenarios with the learning materials for each. The project will produce material in an innovative way by making an individual learning path available to each learner. Through the use of Information and Communication Technologies (ICT), we will be able to deliver learning material that is as flexible as possible. By using a learning material bank, the most appropriate route through the information will be selected and adapted to best suit the needs of the individual learner. Each learner will be able to meet their own individual learning requirements and goals. All the material produced in the project will be placed on-line and made freely available to all interested European educational institutions and enterprises.

The next question asked students to identify what types of learning had helped them learn mathematical logic and how helpful they had been.

Students identified example questions/answers and interactive demonstrations as particularly helpful with 34% and 20% respectively saying “very helpful”. Combining the totals for very helpful and helpful together, these percentages rose to 79% and 63%. 54% of the students labeled course book/textbooks as either very helpful or helpful but other students (46%) labeled them as average, unhelpful or very unhelpful. Lecture slides provided a similar story with a wide distribution ranging from very helpful or helpful (52% of the students) to average, unhelpful or very unhelpful (48% of the students) with the largest percentage (14%) in the unhelpful or very unhelpful categories. Also exam questions and summaries of material were provided a similar way than the book/textbooks and the lecturer slides.

This gives us guidance to the planning materials as a way that students seem to learn best with the help of example questions and interactive demonstrations.

Documents

• Project introduction (short version) - available in PDF format
• Project introduction (long version) - available in PDF format
• Questionnaire - available in PDF format
• Report - available in PDF format