Candidates for leadership positions are often asked: “What do you look for in an excellent teacher?” My response to this question is the ability to teach for student understanding. The learning of knowledge and skill are at the core of education. We want students to deeply understanding the important concepts in all the subject areas. Understanding does not mean that a student can memorize and recite minute facts and demonstrate routine skills with very little understanding. Understanding is more nuanced.

Acquiring knowledge and skill are not synonymous with understanding and does not guarantee understanding. Knowledge and skills can be acquired with little understanding of the underlying concepts of the topic or when to use them. Therefore, knowledge and skills that are not understood do little good. Rote knowledge defies active use, and routine skills (eg. invert and multiple; find the common denominator; listing the American Presidents or knowing the State capitols) are often of poor service when students do not understand mathematical concepts or civics. In short, we must teach for understanding in order to realize the long-term payoffs.

A math teacher asks her students to design the floor plan of a dance club, including dance floors, a place for a DJ, and a bar area. What’s the goal? The floor plan consists of several geometric shapes and a prescribed total area. The students must apply what they have studied about the geometric topic of area to create a sensible plan and explain their thinking that went into the design.

Down the corridor, another teacher asks students to explain about a time in their lives when they had been treated unjustly and a time when they had treated someone else unjustly. These students are reading works of literature, including To Kill a Mockingbird, that deals with issues of social justice. Making connections with students' own lives and creating their own generalizations will be a theme throughout this literature study.

In a science classroom, a student, using his own drawings, explains to a group of peers how a beetle mimics ants in order to invade their nests and eat their eggs. In this classroom, each student has an individual teaching responsibility that includes providing an example to one another that develops a deep understanding of the animal behavior of mimicry.

In an elementary school, students who are studying ancient Egypt produce an on-line National Enquirer style, four-slide power point called King Tut's Chronicle. Headlines announce "Cleo in Trouble, Again?" Why? The format motivates the students and leads them to represent the topic in a new way.

In each case students are asked to critically think through concepts and situations, rather than memorize and respond on a quiz. Teachers are teaching and assessing for understanding. They want more and demand more from their students than remembering the formula for the area of a triangle, or three kinds of camouflage, or the date of King Tut's reign, or the names of the main characters in To Kill a Mockingbird. They want students to understand what they are learning, not just to know about it.

Teaching for understanding is neither easy nor is it particularly welcomed. It is complex and demanding, requiring creativity on the part of the teacher to design the lesson and the assessment. However, it is essential because of the necessity to prepare students for further learning and effectively functioning in their lives.

Critics say: “We are already doing it”; “It takes too long to do within a crowded curriculum”; or "If it ain't broke, don't fix it." Research says differently. Studies of students' misunderstanding of concepts in math include, among a multitude examples: misunderstandings students have from over generalizing rules for one operation and carrying them over inappropriately to another; difficulties in the use of ratios and proportions; confusion about what algebraic equations really mean; and many more. We start teaching fractions in the third grade and we teach the same operations over and other again each year, sometimes for the next seven years. What’s with that? Other examples in science is the denial or misunderstanding of evolution; or the denial of climate change. Studies of students' reading abilities reveal that, while they can read the words, they have difficulty interpreting and drawing inferences from what they have read. Studies of writing show that students experience little success with putting together logical viewpoints that are well supported by arguments. Students write essays by telling what they know about a topic rather than finding and expressing a viewpoint. Students' understanding of history reveals that they suffer from problems such as projecting themselves into another time period and/or a different place. They fail to consider what Truman knew at the time he ordered the dropping of the atomic bomb. Shifts of perspective are essential for understanding history and the understanding of other nations, cultures, and ethnic groups today.

Imagine a gun fight in space. A handful of astronauts fire their guns at one another. What will happen? If you understand Newton's theory of motion, you will predict that by firing the guns, they will be thrust in an equal and opposite direction. The astronauts would soon be hundreds of miles away from one another. Making predictions is a demonstration of understanding, in this case of Newton's theory. Briefly stated, teaching for understanding involves designing demanding ways that students will demonstrate a conceptual understanding though performances. These performances usually involve the student being able to: explain, provide evidence, make a prediction, find examples, generalize, apply concepts, and/or create an analogy or a metaphor, or represent the concept in a new way.

Understanding performances are varied, they must be cognitively demanding; and they must challenge students to reach beyond what they already know. Typically, most activities are routine. To be fair, routine activities have value in teaching and reinforcing newly learned concepts, but they are not performances of understanding. Therefore, they do little to build understanding. Teaching for understanding is a tried and tested approach to raising student achievement.

What follows is a summary of how to teach and assess understanding:

Demonstrations of student understanding include the student: explaining, applying skills and knowledge, providing evidence and examples, predicting, generalizing, and creating an analogy or a metaphor.

• evidence of students explaining or justifying the newly learned concept
• evidence of students adapting, applying, and predicting based on their previous knowledge to create new knowledge
• evidence of students applying newly learned knowledge by giving examples
• evidence of creating generalizations or patterns
• evidence of creating a metaphor or simile that grows out of the concept

  To learn more about Dr. Aronstein visit his website, www.larryaronstein.com