The most drastic change in education is in the area of Mathematics! I was incredibly thrilled to read this conjecture from this online reading titled “Teaching Mathematics in the 21st Century” (http://www.prenhall.com/divisions/ect/app/martinez/pages/Chapter%201.pdf). There have been “math wars”, so the article said, debates on how mathematics should be taught in the 21st century to keep up with the century. And what it said as a product of these “math wars” was… STANDARDS!
Standards will work for me. In my deliberate quest for a way to teach, the trend for 21st century mathematics teaching is to keep up with the standards fought fiercely on expert grounds. Tonight, I have standards to abide by like the stars that shine bright!
I have summarized these so-called standards to seven points, as follows:
- Be ready to “dream big” and help students see that the world is filled with wonderful opportunities because of mathematics!
- Go beyond teaching the basics and model the joy and beauty in mathematics!
- Truly appreciate mathematics.
- Believe that reasoning mathematically can be done by everyone.
- Be truly confident of my mathematical ability and develop it beyond the level of performing the basics.
- Be able to interpret the mathematical worlds that surround us.
- Believe in my ability to teach and the ability of my students to learn
If there is a standard for my role as a teacher in the 21st century, the article also touched on the standard trend on how students should learn. I like that sense of balance. Accordingly, students as per standards should do as follows:
- Be challenged mathematically
- Be engaged in higher-order thinking and problem solving
- Know algebraic thinking, geometry, statistics and probability essentially and not just as add-on
- Focus less on computation but more on meanings and patterns
- Have opportunities to explore and apply mathematics in hands-on and real life
I wondered if the above roles align on purpose with Constructivism. If both contends that students should not learn anymore by drills and memorization but by actively exploring ideas like a scientist with a problem to solve, materials to experiment with and a spirit of cooperative inquiry then the long and short of it is that the trend on math teaching is Constructivism.
The following standards on the curriculum of the 21st century complete the package. The trend for the math curriculum is that it should prepare every student to think mathematically and learn the foundations in mathematical reasoning, concepts, and tools, all are deemed needed for advanced mathematics and for an enlightened living in this age of technology.
Put together, I think that the result will be a classroom as envisioned in the standard which is termed as “NCTM Vision for a Class in Mathematics”. That vision is a classroom where proficient teachers have enough resources and are maturing professionally. The curriculum enables students to perform beyond the basics in a wide range of topics that are approached from different perspectives from which students select. On the other hand, the class have a teacher who help students make, refine and explore conjectures on the basis of evidence. The teacher use a variety of reasoning and proof techniques to prove or disprove conjectures. Students orally and in writing can communicate their ideas and results effectively and they value mathematics and engage actively in learning it. If this is a teacher’s idea of a math class, then he or she abides by the standards. How profitable to know.
With the above, I am beginning to clearly define my teaching philosophy, which is to provide my students with support to learn significant mathematics with depth and understanding. This article has solidified my stand. Profitable indeed!
As an adult educator, I must expect that my students have learned these Content Standards: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability and these Process Standards are Problem Solving, Reasoning and Proof, Communication, Connections, and Representation. I think that these standards are applied like the same ways as the Spiral Curriculum is being applied in the Philippines where each standard is applied across all grades but with incrementing emphasis.
The definitions given below are points of clarifications. I find them very profitable to keep.
- “Problem Solving” means that students are able to build new mathematical knowledge through problem solving where students adapt a variety of appropriate strategies as well as monitor and reflect on the process.
- “Reasoning and proof” means that students recognize it as fundamental aspects of mathematics. Students must be able to make and investigate mathematical conjectures as well as develop and evaluate mathematical arguments or proofs from a selection of various types and methods.
- “Communication” means that students recognize and connect among mathematical concepts toward a coherent whole as well as recognize and apply mathematics to the outside world.
- “Representation” means that students are able to make and use mathematical language to organize, record and communicate ideas to solve problems or interpret physical, social, and mathematical phenomena
- With “Number and Operations”, students should be able to fluently represent and relate numbers, perform the operations on numbers and understand how these operations relate to each other, as well as be able to estimate.
- With “Algebra”, students should be able to understand patterns, relations, fractions and represent and analyze mathematical situations and structures using algebraic symbols.
- With “Geometry”, students should be able to analyze the properties of two- and three- dimensional geometric shapes and develop mathematical conjectures about geometric relationships. Students should be able to solve problems or analyze mathematical situations using visualization, spatial reasoning, modeling, transformations, or symmetry.
- With “Measurement”, students should be able to understand the measurable properties of objects using appropriate unit systems, processes, tools, and formulas.
- With “Data Analysis and Probability”, students should be able to formulate questions that can be addressed with data as well as collect, organize, display, analyze data to answer them. They must be able to select appropriate statistical methods to make analysis or prediction and apply the concepts of probability.
So, how should one define mathematics now? In view of the trends set for the 21st century… mathematics in seven beautiful words is “the study of patterns and relationships”. As an adult educator that is trendy, my role is to help students become familiar with some of those patterns and relationships and to use them in living. Along this line, chase interesting and challenging topics, and that would be trendy.
Another important online reading is the NMC Horizon Report – 2015 Higher Education Edition (http://cdn.nmc.org/media/2015-nmc-horizon-report-HE-EN.pdf). It also tackled on standards.
In 1 to 2 years, the trend will be increasing use of blended formal and informal learning and redesigning of learning spaces. The technologies involved would be the Bring Your Own Device (BYOD) and the Flipped Classroom. The challenges that educators would face were evaluated as “solvable” and will that of blending formal and informal learning and that of improving digital literacy.
In 3 to 4 years, the trend will be on growing focus on measuring learning and proliferation of open educational resources. The technologies that will propel these will be Markerspaces and Wearable Technology. Bringing this trend entails the “difficult” challenge, as evaluated, of making learning personalized and teaching of complex thinking.
In 4 to 5 years, the trend will be on advancing cultures of change and innovation and increasing cross-institution collaboration. These will be propelled by Adaptive Learning Technologies and the Internet of Things. The report evaluated that the challenges ahead will be “wicked” as there would be Competing Models of Education and rewards for teachers.
Each of the above trends, driving technologies, and challenges are elucidated in depth in the report. As an adult educator, my role is to align my techniques and philosophy significantly with Blended Learning, BYOD, Flipped Classrooms, measurement of learning, open educational resources, change, innovations, and cross-institution collaboration. I must construct my own understanding of these, ignite a huge appreciation and be ready for the technologies and the challenges, for the love of Math.