Teaching

 Teaching

An effective mathematics program is based on a carefully designed set of content standards that are clear and specific, focused, and articulated over time as a coherent sequence.

The sequence of topics and performances should be based on what is known about how students’ mathematical knowledge, skill, and understanding develop over time. What and how students are taught should reflect not only the topics within mathematics but also the key ideas that determine how knowledge is organized and generated within mathematics. (See Standard for Mathematical Practice 7: Look for and make use of structure.) Students should be asked to apply their learning and to show their mathematical thinking and understanding. This requires teachers who have a deep knowledge of mathematics as a discipline.

Mathematical problem solving is the hallmark of an effective mathematics program. Skill in mathematical problem solving requires practice with a variety of mathematical problems as well as a firm grasp of mathematical techniques and their underlying principles. 

Armed with this deeper knowledge, the student can then use mathematics in a flexible way to attack various problems and devise different ways of solving any particular problem. (See Standard for Mathematical Practice 8: Look for and express regularity in repeated reasoning.) 

Mathematical problem solving calls for reflective thinking, persistence, learning from the ideas of others, and going back over one's own work with a critical eye. 

Students should be able to construct viable arguments and critique the reasoning of others. They should analyze situations and justify their conclusions, communicate their conclusions to others, and respond to the arguments of others. (See Standard for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.) 

Students at all grades should be able to listen or read the arguments of others, decide whether they make sense, and ask questions to clarify or improve the arguments.

Mathematical problem solving provides students with experiences to develop other mathematical practices. Success in solving mathematical problems helps to create an abiding interest in mathematics. 

This principle says it all.... It isn't about facts, or completing worksheets or even success at tests; it is about  thinking,and analyzing, reasoning and problem solving. The ability to apply, utilize and even synthesize what we know about math. It is truly about looking at math as a life long skill, one that we use everyday in a myriad of ways. This is the expectation at all grade levels. 

This is imposing, exciting and a little overwhelming, but undoubtedly the way math should be taught.

These next pieces deal with pedagogy, the practice of math.... It is the intent of the CCSS to blend the guiding principles of content that we just explored with these principles of practice. The first is learning....

 Learning

Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.

Students need to understand mathematics deeply and use it effectively. 

The Standards for Mathematical Practice describe ways in which students increasingly engage with the subject matter as they grow in mathematical maturity and expertise through the elementary, middle, and high school years.

To achieve mathematical understanding, students should have a balance of mathematical procedures and conceptual understanding. 

Students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought-provoking situations. Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks.

Tasks should be designed to challenge students in multiple ways. Short- and long-term investigations that connect procedures and skills with conceptual understanding are integral components of an effective mathematics program. Activities should build upon curiosity and prior knowledge, and enable students to solve progressively deeper, broader, and more sophisticated problems. (See Standard for Mathematical Practice 1: Make sense of problems and persevere in solving them.) Mathematical tasks reflecting sound and significant mathematics should generate active classroom talk, promote the development of conjectures, and lead to an understanding of the necessity for mathematical reasoning. (See Standard for Mathematical Practice 2: Reason abstractly and quantitatively.)

Wow...... Inquiry Based Learning and Accountable Talk! I feel like this principle is speaking directly to us and telling us that we are on the right path. We have a lot of work to do, but it feels really good that we chose the journey that we did. As you read through it, I would love to hear if you feel the same.