Read the case again, but this time with an eye toward instructional issues. I suggest you keep your class notes handy, particularly: Direct Instruction; Discussion & Questioning. You may discuss the case at your table. Then, without the assistance of cohort members, please complete the following essays:

 

 

 

Describe the various questioning techniques that this teacher used between minutes 10:33-10:54 of the class period.  I suggest you take a tally of the types and frequency of the questions she is asking. Include these specific facts from the case that illustrate the various poor questioning strategies she used. You may critique her responses to student answers too, as this is part of the broader topic of questioning. And be sure to explain the instructional problems that result from this poor questioning technique.

 

    * Be thorough and specific. For example, don’t just say, “She needs to use wait time.” Instead

 describe what wait time is, why it works, and specific ways she could word the question.

 

 

Beginning at 10:33, the teacher attempts to review/re-teach Lowest Common Denominator and Adding Fractions. Her direct instruction strategies are flawed in many ways – in fact, this seems more like a haphazard Q & A than it does a lesson. Many of these problems were addressed in Essay 1, so I am not asking you to describe the problems again. Instead, I want to focus this essay on Direct Instruction solutions.

 

In TTE 536, we learned about effective ways to Present New Material and Provide Guided Practice:

·         Provide schemata to aid students’ understanding of how the information fits together.

·         Be clear in your presentation

·         Keep all students active

·         Use intermittent closure techniques

·         Model

·         Assign practice and Check for understanding

·         Give feedback

 

Select four instructional strategies from the list above that the teacher should have used to make this an effective part of her lesson. Describe each strategy in a distinct paragraph. Be specific. For example, don’t just say, “The teacher should have embedded closure into her presentation.” Instead, define closure and describe specifically how she could have embedded it and why. 

 

 

 

 

TTE 536, Fall, 2009

Instruction Case Analysis

October 29, 2009

 

 

Essay #1: Mrs. Anderson’s questioning techniques included many of the strategies that impede active thinking, and just one of the strategies to promote active thinking. Examples of poor strategies used include:

a.       Allowing students to call out, observed at least twelve times in the 10:33-10:54 time block. The 10:41-10:50 time segment includes a series of called-out answers, beginning with Pam’s answer, “Twelfths.” This is followed by Eric, Pam and Dick each calling out one or more answers. 

b.      Calling only on volunteers, observed at least three times. Examples include Mrs. Anderson calling on Beverly, Heather and Pam, who were noted as raising their hands, at various times and being selected to answer during the evaluated period. 

c.       Calling on the fastest hand up. The observation wasn’t explicit, but it seemed that the three volunteer students noted in item b were also the quickest to raise their hand. 

d.      Naming a student to answer immediately before or after the question. This poor strategy was observed at least ten times in the subject time block. Examples include the beginning of the 10:41-10:50 time block, when Mrs. Anderson asks “What is the lowest common denominator? Ricky?” She calls on him again, and then calls on Randy a few questions later, “So 1/5 would give us how many twentieths? Randy?” 

e.       Asking rhetorical questions, such as in the 10:37-10:41 time block. Mrs. Anderson asks, “And both 7 and 3 will go into 21 an even number of times. Right?”, where “Right?” is rhetorical. A little later she asks, “Does everyone see that?” and gets no response. And near the end of the evaluated period, Mrs. Anderson asks, “Does everyone understand?” At least five instances of rhetorical questions were seen during the evaluated period. 

f.       Relying heavily on choral response questioning. This was observed at least four times, most of them early in the evaluated time block. An example from the 10:37-10:41 time block is the sequence when Mrs. Anderson is demonstrating the first few problems. Several students answer her questions in unison for problems 1 through 4. 

 

Wrong answers were also not dealt with well. Examples include the response to Wanda in the 10:37-10:41 time block when she answered loudly, “It’s 1/7.” Mrs. Anderson replied, “No. Who knows?”   Later, when Cecil answered a question incorrectly, Mrs. Anderson replied “No. You added the denominators. You multiply them. What do you get then?”   Mrs. Anderson’s responses miss the recommendations to dignify the response and assist the student with a clarifying question. 

 

These poor questioning techniques cause students to “drop out” or withdraw from the discussion since they aren’t being actively engaged. The “dropped out” students lose the benefits of constructing content knowledge by talking with others about the material and hearing from other students. The teacher loses the benefit of hearing from all of her students how their thinking processes and knowledge are developing, which could help her know when she needs to adjust her instruction.  

 

The one good questioning technique that was occasionally demonstrated was to call on non-volunteers. Mrs. Anderson did this quite a bit in the 10:47-10:50 time block, beginning with asking Ricky, “What is the lowest common denominator? Ricky?” Several similar questions follow. Out of 44 specific question situations noted in this evaluation period, 7 used this technique.

 

Mrs. Anderson’s questioning techniques would be improved by use of strategies to:

1)      Raise students’ level of concern that they are responsible for giving the answer, and could be called on in class: 

A student might not be too concerned and could choose to “sit out” the discussion if their odds of being selected to answer a question are low. Odds will obviously be zero for some students if the teacher only calls on students who have raised their hands (Safe student strategy: I never raise my hand.). The odds will be still be zero, but students can give the illusion of participating, if the teacher always calls on the first student to raise his/her hand (Safe student strategy: I raise my hand after Pam does, because I know I won’t be called on.) 

 

Mrs. Anderson could increase student engagement and raise their level of concern by randomly selecting a student to answer a question. A tool to select students to call on, such as popsicle sticks with student names on them drawn from a jar, or a random student selector software application, would help her do this quickly and effectively. Random selection will raise the odds of being selected from high for a few students and zero for some students to at least 1 in 25 or 30 for all students.  

 

A refinement to further increase the students’ level of concern is to let them know that you’ll be calling on more than one student to answer questions. By requesting 2 to 4 students to answer the same question, you can raise their probability of being called on to as high as 1 in 6 or so.   Some sources suggest that probabilities above about 1 in 10 are very effective in keeping students engaged with the material. 

 

2)      Provide wait time.

Wait Time 1 is the period after a student is asked to answer a question until the teacher starts to make adjustments such as repeating the question, rephrasing it or asking another student to answer.   Wait Time 2 is the period after a student gives an answer until the teacher reacts or asks another question. Across many cultures and classrooms, research has shown that both wait times are typically less than one second. Research has also shown that 3 seconds of wait time has powerful positive impact on the quality and quantity of student answers, and on the level of student participation in the class. Wait Time 2 is even more important in achieving these improvements than Wait Time 1.  

 

Mrs. Anderson could improve her questioning by allowing more wait time. For example, in the exchange with Pam in the 10:37-10:41 time block about how Pam calculated the lowest common denominator of 1/21, Pam gave an answer “I multiplied.” Mrs. Anderson could have stayed quiet and allowed 3 seconds of Wait Time 2. This would have given Pam the opportunity to further explain her process. This would probably have been more effective to help others in the class understand the concept than the next couple of minutes of short, choppy, back-and-forth questioning of other students that actually happened.  

 

Another example is in the 10:41-10:50 time block, when Mrs. Anderson asks, “What is the lowest common denominator here?” and then “Come on, what about the rest of you? Randy, can you tell us?” Randy doesn’t respond and she continues, “Can someone help Randy? Pam?”    After calling on Randy to answer the question, Mrs. Anderson could have stayed quiet and allowed 3 seconds of Wait Time 1. Randy would have had time to formulate an answer. One article suggests allowing students to say “I pass” if they truly don’t have any answer for a question, and cites research showing that these students are more likely to voluntarily re-enter the discussion during the class period than if they don’t have an “I pass” option.   

 

3)      Give students overt activities to do during wait time. 

When the class is showing difficulty with a concept, or the teacher wants to ensure everyone participates, she can ask a question and then assign everyone a visible activity such as “write three answers to the question” or “turn to your partner and discuss; each pair should be prepared to share two ideas in two minutes.” After completing the activity, everyone in the class should be prepared to answer the question if the teacher calls on them.

 

Mrs. Anderson could have used this method in the 10:50-10:54 time block after providing direct instruction on the method to find lowest common denominators. She said, “So, what’s the lowest common denominator here?” [She points to the three denominators in the problem on the board.]   This would have been a great time to have the students each use a slate to work out the problem individually and show her they know how. Or for them to work individually or with a partner to solve the problem in their notes and then answer the question when called on. So, Mrs. Anderson could have said, “Solve the problem on your slate and hold it up for me to see when you are done.” Or, she could have said, “Work with your partner to find the least common denominator for these three fractions and write them in your notes. I’ll ask for answers in one minute.” And then she could walk around the room to listen to the pairs and see how they are doing. 

 

 

 Essay #2: Four instructional strategies to improve Mrs. Anderson’s attempts to review/re-teach Lowest Common Denominator and Adding Fractions are discussed below.  

1)      Mrs. Anderson should have stimulated recall of the prerequisite knowledge for today’s lesson on least common denominators by using bellwork. Since the class has already been exposed to the material, this could have been worked-out factoring problems with missing steps for the students to fill in, and perhaps some of the vocabulary words for students to define or match up definitions for. This would get students thinking about what they already know that will help them be successful with today’s lesson. 

 

2)      Next, she should have presented the material clearly and accurately. She could have given the students a notetaker to fill in as she lectured and demonstrated finding the least common denominator, to ensure they stayed actively engaged.   She should have planned out her lecture and demonstration to provide well-organized information that will be understood by her students.  

 

3)      After about 8 minutes of lecture/demonstration, she should have provided the students with an intermittent closure activity. This is an activity to allow students to process the new material and organize it in their heads so there is room for the next batch of new information. The closure activity could be something like “Discuss with your partner and write down the first two steps to find the lowest common denominator on a slate. When I call for answers, hold up your slate right under your chin like this.” After a couple of minutes, the teacher will know it they’ve “got it” and students should be ready to continue with her lecture to learn more new material.   

 

4)      A fourth strategy would be for the teacher to provide guided practice for finding the lowest common denominator. Slates can be a great tool for doing this in math classes since the teacher can easily see how students are approaching a problem, where they may be having difficulties, and provide immediate feedback to let them know how they are doing.   A student or the teacher can hold up a completed slate to show the class important points or a novel approach. Depending on the students’ level of understanding, the teacher can make an adjustment to the lesson to extend instruction in this area or proceed with more new material.