Launching a Math Lesson to Increase Rigor and Struggle

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I was speaking with a colleague that teaches kindergarten the other day. She and I were talking about how much kindergarten has changed.  It was just 5 years ago that her days were all about teaching students the alphabet and how to count to twenty.  Now her students are required to learn 60 sight words, count to 100, and know how to make ten with different digits.  The expectations have definitely increased dramatically.

Kindergarten is not the only place that this has happened. I remember when I taught 5th grade about 20 years ago, that our prime goals in math were to master double digit division and multiplication.  Now students are using exponents to explain patterns and to denote powers of 10.  Wow!

I know that to be competitive in today’s world we have to raise the expectations and standards. Students are capable of reaching higher promise. In fact, researchers state that students do better when the expectations have been raised (Boser, 2014).  So, what are we doing to help them to make that reach and fulfill their potential?

Are we rescuing students from higher cognitive thinking?

I’ve been participating in several staff development opportunities lately that have increased my understanding of increased rigor in the classroom. It has been well worth my time.  I’ve also been able to practice the skills I learned in various elementary classrooms within my school district.  I’ve been excited about the results.

 

One piece that has changed my teaching the most is launching a math lesson. Normally, I would glean from students their background knowledge and then proceed to provide them with information that they do not yet have. While determining the students’ schema is still important, I don’t have to shift into delivering the information right away.  I would spend time unpacking our learning target or objective and what they will need to do to be successful.  This will give students a gist of what they will be learning and what they will be expected to do.  I don’t know about you, but I do a lot better when I know that is expected of me.  Why do we not state this to students as well?

After unpacking the lesson’s objective and the ways to success, I can then pose a problem or question that guides the work for that lesson. From there it is very important to make sure that the students understand what is being asked of them.

So often we read a problem to students in hopes to block out language or reading barriers, but then expect them to understand what to do just because we said the words. How many times after that do students then say, “I don’t get it.”  In our frustration, we might respond, “Well, if you were listening you would know what to do.”  But what if the “I don’t get it” statement doesn’t come from lack of listening?  What if the student doesn’t understand what is being asked of them?  Let me give an example.

Teacher asks the students if they have ever been to a bank with their parents. All hands raise.  Then introduces the following problem:

“Mrs. Wilson had $5,000 in her savings account. She earns 10% interest each year.  If she left the money in the bank for a year, how much interest will she earn by the end of the year?”

Teacher reads the problem and asks if there are any questions. No one responds, so she sets the students off to solve the problem.  No sooner does she do this than several students raise their hands to say, “I don’t get it.”

She might ask, “What don’t you get?”

“All of it?” or “I don’t know.”

In frustration the teacher might say, “We’ve been doing this all week. Perhaps you should pay more attention.  Do the best you can.”

The student then stares at the problem and never even tries, which in turn can cause even more frustration from the teacher and student.

 

Does this sound familiar?

Did the student not listen? Maybe. Did the student not understand the English? It was just read to them.  The class had been finding 10% of numbers all week.  This student did fine on the assignment using the algorithm.  This is just putting the math into a story now. Why can’t they be successful here?

Perhaps it isn’t about the math.  Maybe it is more about knowing where to start, understanding the vocabulary, or how the answer should be formatted?  Perhaps, instead, the teacher could have spent some time making sure that students understood all parts of the problem or level the playing field for all students by asking questions about the scenario presented.  When we launch a problem for students to solve, we must take time to clarify the problem.  This doesn’t mean defining every word or telling them what math to use or how to solve it, but rather, enabling students to make the understanding clear together. It’s an opportunity to use student talk and ideas to further develop understanding without embarrassing any student.  Let’s look at that scenario again:

Teacher asks students how they might securely save money. Students might respond with: a lock box, give it to a parent to keep safe, put it in a safe, or put it in the bank. If they don’t come up with the idea of a bank, the teacher might ask further questions to guide them toward that thinking. “Where might a person place their money for safe keeping, but could still get to that money no matter where they were?”  Ideally, a question like this would generate the idea of a bank.  Having images of banks available would also be a helpful tool, especially for ELL students.

Follow this questioning with, “Today we’re going to look at a question that involves money that has been placed in a bank and what might happen to it. Let’s look at that question.”  From there the teacher shows the question and reads it to the class.  Questioning continues with, “What do you notice about Mrs. Wilson’s money?”

Students might respond with, “She has $5,000.” Or “It’s in her savings account.” Or “She earns interest.” And other noticings.

The teacher continues to unpack the problem by asking questions such as:

  • “The problem mentions a savings account. What is meant by that?”
  • “What do you know about accounts at a bank?”
  • “What are you picturing?”
  • “How long does she have the money is the bank, according to the problem?”
  • “It states that ‘She earns 10% interest each year.’ What does that mean?
  • What do you know about interest in regards to money?”
  • “What is the problem asking us to determine/do?”

After a short time, and the teacher feels that the students have a good grasp on the problem, the students can be sent to work on the problem independently, or in a group if more support is needed.

 

From asking questions such as these, you are helping students make sense of all of the information and to discuss, together, any key contextual features of the task, as well as developing common language of the task. All this is done without lowering the cognitive demand for the students.  The questions are asked in a way to elicit students’ understanding and thinking before beginning the technical task of doing the math and to help them gain further understanding of those elements that may block their success as they try to solve the problem.  The teacher has not given the definitions, nor has he/she provided scaffolds that will give clues to how to solve the problem.  This method engages students in applying previous knowledge/learning in a challenging context and making sense of it, but does not rescue them when it gets tough.

By launching the task as a whole group, students also gain understanding through their peers’ thinking. Teachers are facilitating the discussion and understanding, but not providing the knowledge.  The teacher has become more of a coach and less as of a lifeguard who rescues when the student isn’t getting to the answer quickly.  The students are allowed to grapple with the problem together, and then are set out to complete it independently.

All in all, the teacher makes an effort to not lower the cognitive demand by using too many scaffolds or supports, but instead guides the student to their own understanding and pushes them to keep working on making sense of the problem.

As I have engaged students in this type of launch, it has yet to go precisely as I had predicted, but that it okay. They types of conversations that the students have had are fantastic and thoughtful.  The types of solutions we are seeing are much more complex and successful.  And, the numbers of “I don’t get it.” comments have reduced dramatically.  I’m still no expert at this, but I do believe in its potential and will continue to practice this with classes to refine my teaching practice.

More information can be found at: https://connectedmath.msu.edu/classroom/getting-organized/lesson/