Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#11-SUMMATION)

LEARNING EXPERIENCES/KNOWLEDGE ACQUISITION: My approach to assisting children in exercising critical thinking, communication, and observation skills rests in my role as an information  literacy instructor.  My primary responsibility is to support and guide teachers and students in the responsible use and acquisition of information.  This requires that I promote, foster, and facilitate the various forms of logico-mathematical knowledge.  These learning experiences with Ramps & Pathways promote the same thinking that is required for researching and reporting.  Logico-mathematical knowledge is intricate to utilize when searching for and utilizing credible information, extracting necessary details, and synthesizing to report, redesign, and discover new information. 

ENCOURAGEMENT & STIMULATION: I used various statements and questions to spark the students' thinking and encourage productivity.  They are as follows.  "This looks interesting.  Would you explain to me what you have done?  What made you want to move the materials in this way?  If this is not giving you the results you want, what should you do?  Stop.  Look at what you have done.  Where are things going differently than you expected?  How can you fix that?  What do you need to attain the desired results?  Repeating the same process over and over again is not getting you what you want.  So, what should you do first?  Wow!  What have you done here?  Explain what you have built.  Why did you choose to build it this way?  Was their any other way that you could have accomplished the goal?  If this is not rolling back here, why is rolling back here?  What is different here than down here?  What is making the ball roll in the opposite direction?  How are you going to get the ball to continue to roll through the maze of books.  Where is the speed/momentum coming from?  Using the pathways, show me a turn; show me a bend; show me a curve.  This is nice.  I see you thinking.  Let me see more thinking.  What else can you do to be successful here?"

QUESTIONS & EXPERIMENTATION: I responded appropriately and matter-of-factually when interacting with my students.  They did not like the responses I provided in most instances.  They wanted me to give them explicit and direct answers to their inquiries.  In this way, I think they were disappointed with me.  I may have been a bit too encouraging at other times according to Kamii's principles of teaching.  I gave encouragement in terms of "Great!  That looks good.  You did it."  I think I may have done so because the process was difficult and dubious for the students sometimes.  I also recognized that I was irritated often at times.  This was usually provoked by the students' unwillingness to persevere and capitalize on the prompting I provided.  

CHANGES & ENHANCEMENTS: This project was originally created for early learners but because of various schedule and working constraints, I carried out this project with secondary students.  This variation required that I make changes and enhancements to the original project entirely.  Further changes I could have made were to: (1) have the students assign themselves a role during each construction, (2) draft designs for each construction, and (3) further limit the horizontal space the students were allowed to work within. 

LEARNING GOALS MET: The learning goal for this project were met as it was to explore the physical knowledge and logico-mathematical knowledge in children.  This goal was fully met as the presumptions I had about how our students were accustomed to learning were solidified.  It appears that our students are taught most concepts not through thinking-relationships and discovery (logico-mathematical knowledge)-but through identification (social knowledge).

QUESTIONS & ISSUES: The students I worked with lacked serious fortitude, perseverance, and grit in the area of critical thinking.  There were moments that this was painful for the students. This was observed at various intervals during most of the sessions.  Two of the three students actually cried during two separate sessions.  They just were unwilling to take the time and effort needed to think their way through the problems with their construction designs.  I believe this unwillingness comes from a lack of practice and conditioning which has led to low fortitude resulting in an inability to genuinely and authentically learn.  For these students, learning is short term.  It consists of memorization techniques and quick assessments.  It is also very fragile especially when related to self-worth and one's sense of identity.  

Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#10-DIFFERENTIATION 2.0 CONTINUED)

ACTIVITY: I was inspired by another classmates use of drawings and sketches created by students of their constructions.  So, I decided to make this our culminating activity.  Two sessions back, I asked the students to sketch their ideas and thoughts about how they could accomplish their individual goals but I did not photography or capture the ideas they shared on paper.  As a part of this last session, I asked the students to draw a complete design of their intended construction and label its parts.  I was excited to see what creations would come forth.

REMINDER: ALM created a task for BCC to complete which was to (with one ball drop) have the ball roll in three different directions with the last directional roll going to the right.  BCC created a task for CAC to complete which was to (using two balls and one ball drop) have the first ball roll to meet the second ball triggering it to roll in a different direction.  CAC created a task for ALM to complete which was to (with one ball drop) have the ball roll in two consecutive 'Z' formations or zig-zags.

REFLECTION: The students' drawings were much smaller than I anticipated.  They used only a fractional portion of the paper they were provided.  This sort of interested me.  I observed that CAC's drawing looked exactly like her last attempt at completing her individual task.  Somehow (as seen below in the drawing) CAC thought that (1) the slight curving of a pathway was a turn and (2) the second ball should be placed before the turn/curve.  This puzzled me.  She seemed to think that if she started the ball on its path repeatedly that eventually, it would do what she wanted instead of changing the design of her pathway.  BCC created a similar image as CAC and duplicated the same curving of pathways while ALM made substantial gains in her thinking using the drawing, she also missed some intricate aspects in her design.  ALM realized that the balls needed to maintain momentum during the long rolls back-and-forth but only made provisions for this momentum on one side of the entire construction.  This prompted me to ask, "Have you ever done any activities like this in any other classes, high school, middle school, elementary?"

SURPRISES: The biggest surprise that I experienced throughout this entire endeavor was the following statement (in response to my question above).  "NO ONE, NOT ONE TEACHER HAS EVER DONE THIS.  NO ONE HAS EVER ASKED US TO THINK THIS MUCH."  Wow!  Wow!  Wow!  We are responsible for what we complain about the most.  Teachers should know this.  The students fall short because we fell short!

NEXT STEPS:  We have come to the end of this particular project; however, I plan to continue in my efforts to increase logico-mathematical knowledge in these students and others.

Ramps, Pathway & Balls: A Constructivist Endeavor in Physical Knowledge (#9-DIFFERENTIATION 2.0 CONTINUED)

ACTIVITY: Today, the students continued to work on the previous session's assignments.  I added a constraint to the task assigned by each student.  The constraint required each student to construct their pathways using a round wooden table.  Each student was assigned to their own table with an equal amount of working space.  This was done to assist students in utilizing more vertical space rather than the usual act of using more horizontal space.  The pictures below show their initial attempts and final constructions at the end of the session.    

REMINDER: In a twist-up on constructions, the three senior students were asked to give each other a task to complete.  ALM created a task for BCC to complete which was to (with one ball drop) have the ball roll in three different directions with the last directional roll going to the right.  BCC created a task for CAC to complete which was to (using two balls and one ball drop) have the first ball roll to meet the second ball triggering it to roll in a different direction.  CAC created a task for ALM to complete which was to (with one ball drop) have the ball roll in two consecutive 'Z' formations or zig-zags.

REFLECTION: Oh my!  What a quandary I have created!  Thinking is hard work for these young ladies as it seems they are not accustomed to stretching their thinking or pushing forward. The 'grit' exhibited by these students that were needed to complete these tasks was quickly wearing thin.  I feel that these tasks are not too difficult for the students to complete but they lack the motivation to complete the tasks.  They become extremely distracted and unmotivated when first attempts are unsuccessful.  I have also noticed that they respond very negatively in reference to themselves when they have been unsuccessful.  They have made statements like, "I can improve greatly."  "I am not doing very well at this."  "I have to do better."  These are accompanied by deeps sighs and pouting.  Here is where I think encouragement about successful feats is important.  The children know when they are successful or unsuccessful but intermittent encouragement is essential for students displaying waning motivation

SURPRISES: I am surprised at how hard of a blow these activities have been to ALM's and BCC's self-esteem.  I am realizing just how much of our student's self-worth is based on a very limited criterion for intelligence. 

NEXT STEPS: We are down to our last days of this action research project.  I think I will need to work very closely with these ladies to ensure they experience a positive end to this endeavor. 

Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#8-DIFFERENTIATION 2.0)

ACTIVITY: In a twist-up on constructions, the three senior students were asked to give each other a task to complete.  ALM created a task for BCC to complete which was to (with one ball drop) have the ball roll in three different directions with the last directional roll going to the right.  BCC created a task for CAC to complete which was to (using two balls and one ball drop) have the first ball roll to meet the second ball triggering it to roll in a different direction.  CAC created a task for ALM to complete which was to (with one ball drop) have the ball roll in two consecutive 'Z' formations or zig-zags. 

REFLECTION: WOAH!  First, the students appeared to assign (the classmate they were given) with tasks that fit each person's performance level PERFECTLY!  This was quite interesting to me.  ALM was given the most complex task and thus far she has been the most critical and creative thinker of the group.  CAC was given the simplest task and thus far she has struggled more than any other student within the group.  BCC's task was 'middle of the road' just as her performance has indicated.  Like the task that CAC was given, BCC was told to construct a pathway based on past assignments with a little more complexity.  In fact, they all gave each other tasks that were modified versions of the tasks that I had already assigned.  They did not come up with anything original.  I also noticed their continued use of horizontal space.  Not one of these young ladies thought to build up instead of out.  Even when I questioned them and their responses included the use of more vertical space, they kept reverting back to what they were comfortable with doing.  I am not sure if this was them exhibiting a move from what is known towards the unknown or if this was an unwillingness to attempt a task that would require more critical thinking and time for task completion.  (I think they were exhibiting a significant amount of laziness.)

SURPRISES: I was quite surprised by the individual insight the students showed when assigning their classmates a construction task.  I was also surprised at their low threshold for critical thinking, hypothesizing, and processing.  My general consensus is that our students are not accustomed to challenges that activate processes of critical thinking.  Their behaviors suggest that these ladies are accustomed to being taught logico-mathematical logic knowledge as if it were social knowledge.  
NEXT STEPS: Of course the students did not complete their individual tasks today so we will continue tomorrow.  There was a significant amount of jousting and playful banter today hence the unwillingness or inability to focus on the construction tasks.  This will have to be curtailed with increased structure and management.

Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#7-TEAMWORK CONTINUED))

ACTIVITY: This day was part two in the multi-directional task.  The three senior young ladies were asked to use the materials provided to (with one ball drop) have a ball move forward, then in the opposite direction and lastly return to roll in the first direction (a 'Z' formation).  Today all three students worked together to achieve the goal.

REFLECTIONS: The students were a bit reluctant to complete this task.  They have discovered that (as the activities grow more complex) accomplishing the goal is not as easy as imagined.  The students looked at the materials initially (on the first day) and felt that the activities would be child's play.  The more complex the requirements of the construction became, the more hesitation and frustration I observed.  Even with key questioning and assisted analysis, they wanted to quit or let the clock run.  I also noticed that the construction they were creating was a simple extension of their initial constructions.  The students never thought to change the design of the structure.  They simply added to what they created in previous sessions.  The acts of critically thinking, analyzing, readjusting, and hypothesizing were exhausting for these young ladies.  CAC would just watch pleasantly as she reached her threshold while ALM and BCC became annoyed.  With a bit of coaxing, the group did complete the task but with little enthusiasm.

SURPRISES: I was surprised by the rigidity of the students' thoughts.  They were unwilling to try and attempt a new construction to complete the task even though continuing may have been more difficult than trying a new design.  They wanted the task to be easy and the difficulty they faced seemed to challenge their self-image in relation to their perceived intelligence.  This was especially the case with ALM and BCC.

NEXT STEPS: We will have to break tomorrow due to a school activity for seniors.  During our next session, I will have the students assign each other a task.  I believe this will provide some insight into their thinking by allowing them to construct as a teacher or facilitator of learning.

Ramps, Pathways & Balls: A Constructivist Endeavor in Physical Knowledge (#6-TEAMWORK ADAPTATION)

ACTIVITY: Today all three participants (ALM, BCC & CAC) were given the task of extending a previous task by adding another directional change to their pathways activities.  The students were asked to (with one ball drop) have the ball roll in one direction, the opposite direction, and lastly back in the initial direction.  All three students were allowed to work together to achieve the goal set.  Shortly after they began, ALM was called away to the office and did not return before the session ended.

REFLECTIONS:  BCC and CAC appeared to work well together; however, it was not long after they had begun that BCC became highly frustrated.  She began to blow hard, mumble and was reluctant to answer my guiding questions.  She felt overwhelmed and that the task was too difficult.  I asked BCC and CAC about their final thoughts about their experiences and what they feel they are learning from these activities.  CAC responded cheerfully, "You have to use a lot of knowledge."  BCC grumbled about not having the materials needed to complete the task.  I informed her that she was given what she needed to complete the task.  I also assured her that I would never give them a task without the resources needed to complete the task.  (The students were given pathways, blocks, balls, books, and toilet tissue and paper towel rolls.)  After a few minutes, BCC and I discussed her feelings and she admitted that the task was harder than she imagined.  She stated, "This activity requires a lot of thinking and use of knowledge."  She became emotional and expressed dissatisfaction with her performance.  It seems she felt she should have been able to do the task with ease and was rattled when this did not happen. Needless to say, the task was not completed.

SURPRISES: I cannot say that I was surprised by anything that occurred today.  I was most intrigued by BCC's response to her performance.  I think she had an awakening about efficacy and metacognitive abilities as they relate to her self-worth.  I think this is a very clear illustration of how our teaching philosophies, approaches, and pedagogy affects children's LIVES!

NEXT STEPS:  We will continue with today's task tomorrow.  I plan to hover a little more and provide more guidance at shorter intervals.

Ramps, Patheways & Balls: A Constructivist Endeavor in Physical Knowledge (#5-DIFFERENTIATION CONTINUED)

ACTIVITY: The activities today extended from the previous sessions where ALM and BCC worked together to (with one ball drop) have their ball move in one direction and then the opposite direction while CAC continued her work with the initial task of (with one ball drop) having her ball move in one direction and then turn to another direction.

REFLECTIONS: This activity seemed to push ALM and BCC a bit outside of their comfort zones.  I heard a few grumbles and deep sighing.  I translated these as signals for assistance.  Like each day before, I asked guiding questions.  Usually, my questions follow an audible description of what was constructed.  I usually follow, "Where is the problem?  What happens there?  Why is this happening?  How could you remedy the issue or problem?  What would make the ball move where you want or how you want?"  These questions seem to help.  I am finding that the key to their (questions) usefulness is in pressing the "pause button" on their thinking at just the right moment.  CAC continued the same behaviors as with the previous session.  I found myself spending more time guiding her process of construction.  (This can be seen in the video below.)  Everyone was able to complete the goal today.  The atmosphere was a little tense at moments.

SURPRISES: I was greatly surprised that CAC (when asked) would say the problems with her constructions lay in the ball not having enough speed and the pathway needing to be longer.  I was also shocked by her placement of materials that had no real purpose for use as the book under the first ramp in her structure.  (The ages and stages are not lining up!)  I am perplexed and fascinated simultaneously.

NEXT STEPS: Tomorrow, we will embark upon a new challenge adding an additional directional change.