Mathematic educators, parents and students are calling for proper changes in approaches to learning mathematics in high schools. The need to improve learning of mathematics in schools is highly recognized and underlined. Thus, the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics that offered recommendations for high school mathematics reform.
In addition, the Conference Board of the Mathematical Sciences in their official report ‘The Mathematical Sciences Curriculum K–12: What Is Still Fundamental and What Is Not’ stresses the importance of new topics and techniques in the secondary schools. New approaches should develop new learning techniques that would be discrete from statistics, mathematics, and emphasis on algebra and geometry should be properly re-assessed according to different abilities and needs of students who are taking mathematics course in the secondary school and high school respectively.
The need for change and innovation is generally driven by emergence of advanced computing technologies that offers excellent opportunities for school educators to replace manipulative traditional techniques with more complex realistic problem-solving techniques. In its turn, the National Science Board Commission issued a report ‘Educating Americans for the 21st Century’ challenging courses in algebra and pre-calculus and stressing the importance of developing integrated mathematical sciences curriculum in the secondary school.
Researchers argue that new curriculum will positively affect students’ achievement outcomes in the secondary and high schools. To make changes more effective teachers are required to understand the advantage of curriculum’s full scope and its consequences; students are required to support the expectations of classroom environment. The Core-Plus Mathematic Project is newly developed curriculum for high school mathematics. Of course, the Core-Plus Mathematic Project or CPMP curriculum is a matter of debates and controversies as not everyone admits the need of high school mathematics reforms.
Nonetheless, the CPMP curriculum is worked out with assistance of mathematics education researchers, instructional specialists and classroom teachers. Moreover, the curriculum is shaped by empirical evidence gathered from students and teachers who are willing to participate in field testing. In particular, organization of mathematics curriculum should be interpreted in terms of teaching and assessment recommendations and should follow the standards set in the above-mentioned reports.
New mathematics curriculum is a three-year mathematics course for high-school students who are allowed to take the fourth year to prepare for college mathematics. Newly designed curriculum differs from more traditional approaches as new curriculum encourages students’ understanding of mathematics – statistics, probability, algebra, geometry, trigonometry and discrete mathematics. Learning mathematics is developed in focused units that combine fundamental ideas with mathematical habits of mind.
It means that new curriculum stresses the need to connect function, data analysis and symmetry with recursive and visual thinking. In contrast to traditional approaches to mathematics, new curriculum emphasizes the role of mathematical modeling and problem-solving instead of simple calculus. Researchers say the primary goal of curriculum improvement is to enhance students’ understanding and comprehension of key mathematical processes and concepts, to enhance student’s ability to use mathematical concepts in real-world problem-solving.
Graphic calculators should enhance students’ understanding and abilities to solve authentic problems. Improved instructional materials encourage active teaching and learning processes that will primarily focus on problem situations, abstraction and analysis. Oral and written communication, reasoning with ability to represent, and conceptual understanding are highly appreciated and encouraged. All courses centre on mathematical reasoning and thinking with abilities to develop formal proof.
Additional fourth year course will allow to keep students, who prepare for college mathematics, despite whether their undergraduate program is based on calculus. Students interested in mathematics are encouraged to be accelerated into the fourth course year. Today, many researches are focus on identifying whether new curriculum meets its specific goals. In particular, they try to reveal whether the learning outcomes based on new patterns of mathematics learning process differ from outcomes based on more traditional curriculum.
During the past eight years researchers conducted various studies to examine mathematical achievement in classroom with CPMP curricula. Research studies have revealed that performance of CPMP students is much better than that of students with traditional interpretation of mathematical representation. It means that problem-solving and recursive thinking appear to be more effective in learning mathematics than simple understanding of key concepts of processes. Further, CPMP students are characterized by higher grade results at the end of the years than students with traditional approach to mathematics.
Summing up, recent researches have indicated that CPMP students perform better than students with traditional curriculum. CPMP students are characterized by better abilities to interpret mathematical representation and calculation, to measure conceptual understanding and to recognize the importance of problem-solving. CPMP students are better in probability and statistics, algebraic manipulative skills, etc. Nonetheless, researchers argue that student’s success in college mathematics doesn’t fully depend on CPMP curriculum.
Other factors, as, for example, student’s attentiveness, readiness to participate in learning process, self-awareness, classroom environment, play their important role in student’s high school mathematics performance. With guidance from educators, researchers and teachers, curriculum developers will be able to build on stronger patters of student outcomes.
Schoen, H. L. , & Hirsch, Ch. R. (2003). Responding to Calls for Change in High School Mathematics: Implications for Collegiate Mathematics. The Mathematical Association of America Monthly, February, pp. 109-123. Available on-line from http://www. jstor. org/stable/3647770 .