“Instructional Strategies” Due Oct 19

Assignment from Syllabus

Instructional Strategies (3)

You should observe as many class periods as necessary to document the use of three different instructional strategies. These observations may or may not be conducted in your endorsement area(s). Summarize the instructional strategies used. How did the instructional strategies enhance student learning and engagement? Were the instructional strategies used effective for reaching the learning goals? What could have been done differently?

[from BlackBoard]

Instructional Strategies

Posted on: Wednesday, October 12, 2011

Here are some examples of instructional strategies you might look for this week:
Small group discussion
Whole class discussion
Use of examples and non-examples
Socratic seminar
Acting out a problem
Review game
Graphic organizer
Group investigation
Guided practice
Use of manipulatives
Identifying similarities and differences
K-W-L Chart
Panel discussion
Gallery walk
Carousel brainstorming
This list is not comprehensive. Good luck 🙂

I observed the following strategies on 10/18/2011 during 3 Algebra courses at Mt. Rainier High School (Des Moines, Highline School District).  Teacher was Mr. B.  Textbook being used is Discovering Algebra:  An Investigative Approach by Murdoch, Kamischke & Kamischke.  Mr B. has taught for 20+ years, has helped start middle schools and high schools, and has also taught previously at a Big Picture school.

Strategy #1:  Journaling

Summary:  Students are asked to write about what they have learned in full sentences in addition to note-taking.  Examples:

o     After an in-class lecture/review on the use of an x-y table to compute and then plot values of an equation for a line, students are asked to “turn to a blank page in your journal and write five thoughtful sentences describing something you have learned”.  Mr. B gave an example of a sentence.

o     Students working in pairs are asked to have one student fill out an x-y table while the other student describes in words the steps that the first student is following.

o     Worksheets probing student understanding of equations of lines are asked to convert graphs, equations, recursive routines, and tables into “stories” about that equation.  For example:  “Maria burns an average of 150 calories in her workout and then 200 calories for each mile she runs, the total calories she burns in a workout as a function of miles run is …”

o     Thursdays are reflection days where students will be asked to produce a paragraph describing what they have learned over the prior week.  They are allowed to use sentences in their journal over the prior week to construct that paragraph.

o     By the end of the year (June 15) students are asked to turn in a 10-page paper describing their answer to the question “Who am I”.

Engagement/Learning:  Students in class appeared to be engaged in the activity of journaling, although I wasn’t able to walk around and view what the whole class was writing during this activity.  The bigger question is whether learning is achieved through the journaling.  I wasn’t able to tell that based on one visit, so I will have to schedule a follow-up to see if students journaling about interactions with equations of a line were more able to meet learning goals for that unit.  I am also curious how these journals are used in overall assessment, and how journaling-type questions on tests are graded.

Effectiveness: This observation prompted me to start a mini-literature survey on effectiveness of journaling in mathematics classes.  While Arnold (2011) reports mixed results (in a somewhat flawed study) for effectiveness, Dougherty (2002) writes extensively about how to use journaling effectively in mathematics classrooms. 

Suggested improvement:  A central criticism for verbally intensive books and classroom techniques is to provide reasonable scaffolding for ELL students.  For students with special needs that prevent writing longhand or cursive (and math too?) other methods should be found to get at how a student is synthesizing mathematical concept and procedure (audio, video, simultaneous translation?).


Arnold, H. I. (2011). The Effects of Prompted Math Journaling on Algebra 1 Students’ Achievement and Attitudes. In L.P. McCoy (Ed.), Studies in Teaching 2011 Research Digest (pp. 5-10). Winston-Salem, NC: Wake Forest University.

Dougherty, B. J.,  (2002). The "Write" Way: Mathematics Journal Prompts for Algebra I. Honolulu, HI:  Curriculum and Development Group.  Retrieved from EBSCOhost.

Strategy #2:  Add-To Exercise (White Board, Whole Class, Review of Prior Material)

Summary:  A student is selected/volunteered to go to the board and write a concept or problem from the prior day’s notes.  Another student is asked to add to that, and so on until the initial starting point is exhausted.

Engagement/Learning:  This technique allows for deep but individual student engagement.  Since students don’t know who is going to be called/volunteered next there is some apprehension.  However, once a student is at the board and starts writing, engagement starts to drop off.  In the best case, students are able to check their notes against a conglomeration of a priors days notes as it is reconstructed from multiple sources on the board for all, including the teacher to see and correct if needed.  If we grant that demonstrating a concept for peers improves learning (for at least some) then this method could be quite effective.

Effectiveness:  During my observation I observed a couple of things that might hint at a lack of effectiveness.  If the goal is demonstrating legible and accurate approach, then a lot can happen when you give a student a whiteboard and a dry-erase pen.  Right of the bat the student wrote 2x+3=9, sat down and then a few moments later yelled, “I forgot the ‘y’, it should be 3 times y”.  We solved the first problem together, then added a y and solved the next problem.  As we solved the first problem (without the y), it took a couple of students helping each other to get through the solution steps and do the arithmetic right.  During this time it was hard to gauge what other students were learning in the process.  Some students would comment on errors or perceived errors—which weren’t actually errors but just subtle differences in style, e.g. multiple by –1 on both sides or divide by –1?   Arguments can ensue over the most trivial of notational differences.  As we worked on the correct version of the equation, i.e. 2x+3y=9, the correct solution was written up, disagreed with by a vocal student, driven to erasure, and then they went up front and wrote their own solutions steps with some non-standard notation.  That was after Mr. B. asked her to write larger so that he could see from across the room.  Students tend to stand in front of what they are writing as well, out of embarrassment or desire to work the problem for themselves and not to share with others.

Suggested improvement:  A document projector instead of white board might be more effective.  Running the document reader from the back of the room while the teacher points out things on the projected copy communicates that student is presenting for students, and teacher is up front commenting as authority on what is written.  On a document projector the issues with whiteboard not being a standard place for students to write, so it starts off more familiar, students are writing on a horizontal surface not vertical, and correcting and size of writing are not so much of an issue.  That is all procedural changes, but yet improvements that reduce the pedagogical friction of the process, so that the learning/understanding could be front and center.  I am completely willing to try a less contentious procedure for how to do this activity.

Strategy #3:  Group Work, Demonstrations in Groups, Small Teams

Summary:  I observed Mr B. in an Algebra lesson demonstrate the solving of a simple equation on the board.  He then wrote another problem on the board and asked students to solve that problem in small groups around their tables.  Once he was sure that most groups were on track he was able to focus on a smaller group that was having more difficulty.  For that group he grabbed a small whiteboard and proceeded to repeat the demonstration on the new problem but at the table with learners having difficulty.

Engagement/Learning:  Since the other groups were able to work off knowledge gained from the larger group, it definitely improved the engagement for the struggling group to have the teacher there in close physical proximity.  As far as learning, Mr. B. in the smaller group was able to make sure that students were taking notes about the second demonstration, and he was able to do verbal probes for each student to make sure they were taking things down.

Effectiveness:  If the larger group of students already working in their groups were truly on task and completing the 2nd problem, then by doing another demonstration in a smaller group, Mr B. effectively addressed the gap in the learners abilities.  If however, the groupings had more distributed learners that were struggling then they would have to rely on other students in their groups who were knowledgeable in order to keep going on that example.  Put another way, if the group of struggling learners was larger than the group Mr. B. was focusing on, then this approach could have been improved.

Suggested improvement:  Initially I really liked the group work strategy, and then it seemed natural that one group might be struggling more than the others, so Mr. B. would go to that group and do a more tailored demonstration to that group.  However, when I saw that the other groups really got no occasional visit from Mr. B. as he focused on the group of struggling students, I wondered if distributing the struggling students more uniformly wouldn’t break them out of some behaviors they have and reinforce amongst themselves when they are together.  It seems like Mr. B. might still have to visit each struggling student in turn, had they been distributed to separate groups, but perhaps the other groups might have better served the purpose of another demonstration with support.

Other notable interactions from these classes I observed.

Mr B. is also a coach and uses some hand-clapping prompts to pull students back from a group activity (or general restlessness) into a more uniformly coherent, and  attentive state.  “Give yourselves 1” prompts students to clap once and based on the intensity or uniformity of the sound Mr. B. can tell if students are actively paying attention.  If they are, he proceeds.  If class is not together or attentive, he prompts again with “Give yourselves N” where N is some other number that prompts a handclap, the larger the number N, the more complicated the series of clapping, lap/table slapping, arms folded with hands on opposite shoulders, etc.

Mr. B. will often ask if students have comprehended what they will be doing in a class activity that he has just described.  He gauges the extent of comprehension by the way the hand has been raised, saying “if you arm is bent at the elbow, your hand is not raised, are you sure you understand what is being asked of you in the next activity”.  If he is not satisfied he may repeat the instructions.  I did not see him call on a student and ask them to repeat the instructions, don’t know how much use that would be…

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  • mcacciapuoti  On October 26, 2011 at 1:37 am

    I like your idea in the suggested improvement for the group work, small teams observation. I find myself falling in that trap occasionally because some groups tend to struggle more than others. I would like to redistribute the students, but at this point in the year it’s not up to me yet.

  • Amy Vaughn  On October 31, 2011 at 2:40 am

    I like that you referenced research for journaling. Dr. Art Ellis, a professor at SPU, is internationally known for his research in reflective practice, including journaling. He’s a brilliant man; you might enjoy talking with him over coffee…

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