Friday, July 2, 2010

Mathematics Teaching in Ghana; Is it the Problem?

Development in almost all areas of life is based on effective knowledge of science and mathematics. There simply cannot be any meaningful development in virtually any area of life without knowledge of science and mathematics. It is for this reason that the education systems of countries that are concerned about their development put great deal of emphases on the study of mathematics. In Ghana, mathematics is a compulsory subject at all levels in pre-university education. Due to its importance the government is committed to ensuring the provision of high quality mathematics education.The main rationale for the mathematics syllabus is focused on attaining one crucial goal: to enable all Ghanaian young persons to acquire the mathematical skills, insights, attitudes and values that they will need to be successful in their chosen careers and daily lives. The new syllabus is based on the premises that all students can learn mathematics and that all need to learn mathematics. It is therefore designed to meet expected standards of mathematics in many parts of the world. At the Senior High school (SHS), the mathematics syllabus builds on the knowledge and competencies developed at the Junior High School (JHS) level. The student is expected at the SHS level to develop the required mathematical competence to be able to use his/her knowledge in solving real life problems and secondly, be well equipped to enter into further study and associated vocations in mathematics, science, commerce, industry and a variety of other professions.

In spite of government efforts, mathematics has not undergone much change in terms of how it is presented. These reflect consistently in low achievement levels in mathematics among students at the SHS’s and JHS’s. Results from the Trends in International Mathematics and Science Study (TIMSS); an international study conducted by the International Association for the Evaluation of Educational Achievement (IEA) of the USA in 2003 and 2007 at the JHS level (grade 8 equivalents) are instances of poor mathematics achievement in the country. In the aforementioned study, Ghana’s 8 graders were ranked 43rd among 44 and 46th among 47 countries that participated in the study in 2003 and 2007 respectively. The situation is not too different in the SHS’s. For many years the failure rate in mathematics has been dramatically high at this level. The low scores of students’ over the years in the Senior Secondary School Certificate Examination attest to this. As a result many students are unable able to pursue higher education after graduating from the SHS because they failed in their mathematics examinations.

The teacher factor is considered one of the prominent reasons for students’ poor achievement in mathematics. In Ghana, the approach of teaching mathematics is mainly teacher centred which is characterized by transmittal techniques (chalk and talk, dominated by teacher talk), making students to completely depend on teachers. With this teaching approach, students can use formulaic algorithms, but they rarely internalize and develop deeper insight into the mathematics they are learning. But should we be quick to blame these mathematics teachers? Obviously, the answer is no; these teachers also have been taught in the same manner and for most of them adapting new methods for instruction to enhance mathematics learning is a complex innovation.

What could be done ?
There is no doubt that something needs to be done! Students must understand mathematics to the extent that they see how mathematics ensures efficiency in all human endeavours, especially how it applies to their future professions. This is possible if the study of mathematics is made less stressful and mathematics itself becomes meaningful and relevant to those who study it. For this reason, it is very important that teachers of mathematics are sensitised and equipped to provide opportunities for their students to enjoy the study of mathematics and be good at it.
Recent research findings from mathematics education show that integrating of ICT changes the nature of teaching and learning. ICT seems to provide a focal point which encourages interaction between learners and the technology itself. This implies that ICT used in instruction support constructivist pedagogy, where learners use technology to explore and reach an understanding of mathematical concepts. However, for ICT to be used effectively in everyday teaching, radical changes are advocated in approaches to teaching. Teachers must adapt to new roles.

My vision
I have a vision therefore to support mathematics teachers in this transition. I am committed to providing professional development and training needs which will assist mathematics teachers to integrate technology in their teaching practices. Also to be promoted are enrichment programmes for mathematics teacher education which will incorporate ICT to help train pre-service teachers to be able to use technology in their future classrooms. I have conducted a number of studies particularly in Ghana and in this page I post reports of some findings.

The Overview of the study:
The research is meant to contribute to improving teachers’ teaching in the secondary schools. It is expected that the study will bring about an improvement in the teaching/learning by making mathematics pre-service teachers more critical of their teaching in order to help learners to improve their thinking skills in general and mathematical concepts in particular. The study will also serve to improve teachers’ actual use of ICT resources, thereby helping to contribute to bridging the gap between curriculum intentions and actual practice. The target group of pre-service teachers would be equipped with technology integration skills and knowledge for their future careers as professional teachers at the pre-tertiary level. The study was conducted in different stages. I discuss the main concerns of the studies as were addressed in the various stages.

Stage 1: Feasibility of ICT use in Ghanaian Mathematics Classroom
In this particular study, I tried to explore the situation in Ghana to see the possibility of using ICT in instruction in mathematics classroom and what kind of support mathematics teachers need to be able to integrate ICT in their teaching. The relevance of this study was to (i) provide an understanding of the context of mathematics teachers in the SHS’s in Ghana regarding ICT integration in mathematics lessons and (ii) determine the features of an ICT intervention that fits the realities in the SHS’s that can prepare pre-service teachers to effectively design and implement ICT in teaching mathematics. Questions such as:
1. What are the barriers of ICT use in teaching mathematics in SHS’s in Ghana?
2. What are the needs of pre-service and in-service mathematics teachers in teaching mathematics with ICT in SHS’s in Ghana?
3. What are the opportunities of ICT use in the teaching of mathematics in SHS’s in Ghana.
were asked. A total of 180 educators constituting of 60 practicing mathematics teachers and 120 pre-service mathematics teachers participated in this study. The practicing teachers were selected from 16 Senior High Schools (SHS) ranging from government, mission, private and international schools. The results showed that lack of ICT facilities in SHS’s was not the major barrier of teachers as far as integrating technology in teaching was concerned. However lack of knowledge to integrate technology into their teaching and lack of training opportunities appeared to be the major concerns of the teachers. Preliminary analysis confirmed that the government of Ghana and other institutions had invested huge sums of money in procurements of computers and establishment of computer labs in most Senior High Schools (SHS,s) following her ICT for Accelerated development (ICT4AD) policy to introduce information and communication technology (ICT) into the school curriculum at all. The findings reported directed attention to areas that require further attention to enable teachers use ICT in mathematics teaching. In particular, a professional development scenario that will assist pre-service teachers develop skills on ways to integrate ICT in their teaching processes was one of the significant issues identified by the researcher. Bearing in mind the complexity of the problems mathematics classroom in Ghana face in terms of ICT infrastructure and lack of application software, an environment with a more generalised application that offer a technology readily available and user friendly among mathematics classroom with the potential for supporting students’ higher-order thinking in mathematics (such as spreadsheet) was proposed for use in such a professional development programmes. The study also showed that opportunities for such a programme existed. First of all policy documents highlight the importance of integrating ICT into the curriculum at all levels. Curriculum documents in this context suggest that teachers should start every lesson with a practical problem to help students acquire the habit of analytical thinking and the capacity to apply knowledge in solving practical problems and also make use of the computer for problem solving and investigations of real life situations.

You will find the abstract and more details of this report here and here.

Related to this study is another study on Exploring the potential of the Will, Skill, Tool model in Ghana: Predicting prospective and practicing teachers’ use of technology.
You can find the abtstact of this report and the full text here and here.

Thursday, July 1, 2010

Stage Two- Designing a Professional Development


As a follow-up of the recommendations from the first study, a professional development programme was organised for mathematics pre-service teachers from the University of Cape Coast in a pilot study. The main idea behind the pilot study was to get the practice of working with a preliminary design that will ensure the validity and practicality of an intervention to integrate technology among these mathematics pre-service teachers in the long run. Further more this stage was to test out any uncertain aspects of the procedure to be sure that it will work as intended in a main study (stage3). The framework that was used in this study was TPACK. Technology, pedagogical and content knowledge (TPACK) describes that body of knowledge that teachers need for teaching with and about technology in their assigned subject areas (such as mathematics) and grade levels (See the figure) .

The professional development approach that was used was the Teacher Design Teams (TDT). The design team (two teams) consisted of four pre-service mathematics teachers from the department of science and mathematics education programme at University of Cape Coast (UCC), with extra help and support from different external tools such as workshops and two different kind of support system, human support (the researcher) and exemplary materials. Findings of this stage are reported in the paper: Developing Technological Pedagogical and Content Knowledge through Teacher Design Teams: The Case of Mathematics Teachers in Ghana. (see the abstract below)

Abstract: Although many studies have shown the need to better align teachers’ preparation in the integration of technology in classroom practice, most teachers in Ghana have not had any preparation that develops their technology pedagogical and content knowledge (TPACK).This paper presents a case study of four mathematics prospective teachers at the University of Cape Coast, Ghana. The teachers worked in two design teams to develop lessons and subsequently taught in a technology-based environment for the first time. To make them familiar with technology use in mathematics teaching the teachers first discussed and used exemplary lesson materials, which were prepared by the researcher. Based on this experience the teachers designed their own technology-based lessons, which they taught to a group of teachers. Interview, observation, and survey data were collected throughout the study. The study revealed key attributes of a professional development scenario to foster growth of teachers in TPACK.

You can find full versions of the quadratic lessons the two teams designed here and here.

Knowing how to use technology is not the same as knowing how to teach with technology- Mishra and Koehler (2006).

The slides for their presentations can also be found here and here.

Stage 3: ICT integration in typical Mathematics Classrooms

Tuesday, June 29, 2010

SITE 2010 - San Diego, CA

The Society for Information Technology and Teacher Education (SITE) is an international association of individual teacher educators, and affiliated organizations of teacher educators in all disciplines, who are interested in the creation and dissemination of knowledge about the use of information technology in teacher education and faculty/staff development. SITE members learn about, and contribute to, the latest developments, techniques, and concepts in teacher education and instructional technology.
In SITE 2010 it was great to be part of a symposium: “Strategies for teacher professional development of TPACK” organized by Joke Voogt of Twente University. The symposium consisted of 4 different presentations by faculty and graduate students from different universities (Twente University, Michigan State University, Iowa State University and University of Cape Coast) demonstrating how TPACK has been used in different context to assess teachers’ integration of technology. Though it was my first time at SITE, it was a wonderful conference and the various presentations at this symposium gave me a deeper insight on the usefulness and applications of TPACK.

You can access the proposal for the symposium. In this page also I post the various abstracts of the presentations.

Developing TPACK through teacher design teams: The case of pre-service mathematics teachers in Ghana - Douglas Agyei.

Abstract: Although many studies have shown the need to better align teachers’ preparation in the integration of technology in classroom practice, most teachers in Ghana have not had any preparation that develops their Technology Pedagogical and Content Knowledg (TPACK).This paper presents a case study of four mathematics teachers at the University of Cape Coast, Ghana. The teachers worked in two design teams to develop lessons and subsequently taught in a technology-based environment for the first time. To make them familiar with technology use in mathematics teaching the teachers first discussed and used exemplary lesson materials, which were prepared by the researcher. Based on this experience the teachers designed their own technology-based lessons, which they taught to a group of teachers. Interview, observation, and survey data were collected throughout the study. The study revealed key attributes of a professional development scenario to foster growth of teachers in TPACK.

You can access the slides for the presentation below and the full text here.
Technology Integration in the Science Teachers Preparation Program in Kuwait: Becoming TPACK competent through Design Teams-Ghaida M Alayyar.

Abstract : The research studies the integration of technology in the science teacher preparation program in Kuwait at the Public Authority of Applied Education and Training (PAAET) aiming at preparing prospective teachers to work in the school of the 21st century. The TPACK framework is used as a starting point for designing a course where prospective student-teachers are prepared to integrate technology in elementary science education. In the course a group of 50 science students had to design and implement a technology application in small groups (3-4 persons) for elementary science education. During the design the small groups were coached by subject matter, pedagogical and
technology experts. Data were collected on students’ TPACK competencies (Schmidt et al. 2009), their attitudes towards technology, their perception on collaborative group work, their appreciation of the new course and the quality of their products.

The Development of an Instrument to Assess Teacher Development of TPACK Denise Schmidt, Evrim Baran,& Ann Thompson, Iowa State University.

Abstract: A research group including faculty and students from both Michigan State University and Iowa State University have been working on the creation and validation of an instrument designed to assess the development of TPACK in pre-service teachers (Schmidt et al., 2009). Current work on the instrument will be shared. The instrument is used at the beginning and end of an introductory pre-service teacher technology course. Results suggest that with a minor modification of the survey items, the survey is a reliable and valid instrument that will help educators design longitudinal studies to assess pre-service teachers’ development of TPACK. Results also indicated statistically significant gains in all seven TPACK components.

Developing TPACK by design in a Master’s Program-Punya Mishra, Matthew J. Koehler, Tae Seob Shin, Leigh Graves Wolf, & Mike DeSchryver, Michigan State University.
Abstract: As evidenced by Koehler and Mishra’s (2005) study, the “learning technology by design”is an effective instructional technique to develop deeper understanding of TPACK. In this study, we introduce an intense educational technology course sequence designed to create an experience that would expose in-teachers to ideas and skills from educational technology that can be incorporated into their own teaching. These experiences happen in cohort based summer study programs with students who are experienced educators. These programs include a unique face to face context in Europe in and a hybrid format for in-state educators. During the course, participants worked on a range of assignments that required them to learn and use technology in multiple pedagogical contexts including developing digital video, writing a technology based grant proposal, exploring web 2.0 technologies, and designing a personal web portfolio. The analysis of pre and post-test data showed that in-service teachers’ understanding of TK, TCK, TPK, and TPACK improved as a result of their course experience.

The entire slides for the symposium can be found on Punya Mishra's blog. More details of SITE 2010 can be found on Petra Fisser's blog.

Thursday, June 24, 2010


The Utrecht Summer school is a program organized by Freudenthal Institute for Science and Mathematics Education (FIsme) in the Netherlands. The aim of this program includes bringing participants up-to-date in curriculum development and research in the field of science and mathematics education. It also includes refreshing and deepening the knowledge in core subjects of various fields of Science and mathematics. (For more information of the Utrecht summer school, see ) .
In the 2008 Summer School it was really a pleasure for me and colleagues from different part of the world (mainly Asia, Africa and Europe) to discuss the principles of Realistic mathematics Education (RME) to think about ways in which students can learn mathematics meaningfully. For pictures of the Summer School 2008, see: In this page i post summaries of activities of various workshops, presentations and interesting concepts in mathematics teaching particularly for the primary and secondary schools.



RME: An approach towards the learning and teaching of mathematics developed by the Freudenthal Institute, Utrecht University, the Netherlands(

Started around 1970
* Not affected by “New Math”-movement
* Freudenthal said: “New math” uses anti-didactical inversion: the endpoint of the work of mathematicians (e.g. set theory as organizing tool) is used as a starting point for instruction.
* Alternative: mathematics as a human activity:
- organizing subject matter from reality
- ‘guided’ opportunity to ‘re-invent’ by doing
* Focus: on math as an activity, on the process of mathematization, not on math as a closed system . You can find examples in the clip following.


Teaching-strategies should involve:

Do not introduce new formula’s were they are not needed! Relate to the students’ common sense and to what they know already; use what they know rather than adding a new formula to their knowledge…..

Start a new topic with preferably a context in which the mathematical topics get a meaning. Give time for exploration!

- E-C-R: Estimation – Calculation – Reflection
A very useful teaching-technique, that can be used for a lot of topics. By using it, a ‘feeling’ for numbers and measurement will be developed.
If this technique is used all the time, a student will know that something went wrong if he wrote:
47.01 - 0.65 = 22.1, or 6.25 – 4 = 6.21 . Some examples in "Distance between two points" and "Angles" can be found here and here.

To encourage reflection on activities done by students, there are three ways you can use being the teacher:

1) by asking different kinds of questions:
(i) reflective questions: “what happened here?”
(ii) predicitve questions: “what happens next?”
(iii) open questions: “can you do this in more ways, you think?”
(iv) mirroring questions: “So if I understand you correctly, I hear you say: ….. Is that what you mean?”

2) by having the students report orally: the teacher requires the students to report back from what they have done. The students then think about their activity for the best way to talk about it. (And you will still use your questions during their reports!)

3) by having the students report in writing: the teachers directs the students to record things that come up from questions. The students draw and write (using their own words) in their notebook what they think has been discovered .

You use these types of questions to help the students structurize their way of working in a way that is understandable for more people. So an actual situation would be that students are working on assignments in class, you are walking around and you want to know what the students are doing, or how they are thinking; you want them to reflect on their thinking.

If you are really interested in what your students are doing, you will ask ‘the right’ questions without realizing what kind of questions they are!

WHY do you think that is the answer? HOW did you come to that answer?
Actual situations in which these types of questions accour is when you are interactive with your students, discussing exercises, or questions about a (new) topic, etc.

(f.i. in textbooks)

Low-level questions:
one-level questions, all information needed is in the question, there is only one way to solve it.

Problem 1: “We went for a ride in the car. We drove 231 miles and had to fill up at the petrol station. The tank took 14.3 gallons. How many miles per gallon did we get?”

High-level questions:
More steps have to be taken before you can find the answer, you can probably derive all information from the given but it is possible that you have to do some reasoning before you have that information, there are different strategies to get to the answer.

Problem 2: “We have driven 2/3 of the journey and the tank is still ¼ full. Do we have a problem if we don’t fill up?”

There is also the difference in WHAT-HOW-WHY-questions.
WHAT (WHEN, WHERE) – questions are called “fact-questions”
HOW-questions are called “partly fact, partly thinking-questions”
WHY (WHAT IF) - questions are called “thinking-questions”

In mathemaitcs-textbooks however, these words are not used all the time, so you should really take a look at what kind of activity is asked from the student in answering the question.

In the post below i present some common examples teachers experience in mathematics lesson as were discussed in this summer school.

For more information on how you can participate in this school in the coming years you can contact:
Jaap den Hertog

Coordinator Summer School

Utrecht University
Freudenthal Institute
for Science and Mathematics Education