GROWING THROUGH OPEN QUESTIONS

GROWING THROUGH OPEN QUESTIONS

Many math-minded people, me included, have difficulty with open questions.  Open questions have no true solution.  We silently scream to the math gurus, “It is supposed to have a solution!”  We have a need to find the answer.  It is why the concept of an open question is very foreign and often times scary for math teachers.

I recently watched a Building Math Minds video called, “Why Teaching with Open Questions Makes all the Difference.”  The presenter was Marian Small.  In this video, she explains why open questions are perfect for math instruction.  I must admit, I agree.

She starts with giving some examples of an open question.  “________ is 4 times as much as ______________.  What could go in the blanks?”  Once her students have had an opportunity to fill in the blanks, she asks questions about the numbers, not asking the students to reveal the numbers.  Some of the questions she asked for this example were: Which number is larger?  Could the numbers have been equal?  Could the first number have been 20?  Could the second number have been 20?  How about 21 for the second number?  The answers to these questions are all yes.  If the numbers are not equal (0), then the second number is larger than the first and first number is always 1/4 of the first.  In this question, the students are able to choose any number for the first spot and then calculate second.  Another concept learned through this exercise is that if the student uses a whole number, then the second number will be even.  

One of the greatest points she made is that open questions have built in differentiation, as the students answer the questions based on his or her own abilities.  If one student is advanced and chooses 1/4 as his starting number, the second number will be 1.  If a child starts at 1, his second number will be 4.  Each is correct and each is within the ability of the student.  Differentiation becomes necessary, when the teacher fills in one of the numbers.   Further, once the teacher chooses a number, it is no longer an open question, but an equation to be solved.

Another benefit of the open question is the opportunity for rich conversation.  Math talks are a wonderful way for students to learn and grow.  A student that can logically explain why he or she reached an answer is learning number sense and not just operation sense.  Number sense is more than working out problems.  It is knowing that 111 is 100 + 10 + 1, 100 is 10 10's, 10 is 10 1's and 1 is 1.  These concepts are as necessary for students to develop, as it is for them to learn to read.  Reading begins with learning sight words.  Math begins with learning the numbers, place value and number sense.  These concepts are the building blocks for greater success in advanced level courses.

Finally, she discussed how she creates her open questions.  Each question is created by first reading the standard, then thinking about how it could be used in an open question.  She chooses words that allow for wiggle room, such as “a little more,” “a little less,” “close”, or “almost”.  These words do not have actual numerical equivalents and therefore allow for more answers to be correct.

An open question allows students to show what they have learned and that they can use their knowledge.  It also allows each student to answer, as he or she is able.  The built in differentiation element allows for multitude of answers and rich conversation for all students in the classroom.  A problem without an answer is a wonderful thing.  Who knew?