Science Inquiry Project - Volcanoes

Woodmoor Elementary

A few weeks ago, a cohort member and I had the opportunity to meet with four 3^rd grade students from Woodmoor Elementary; Shay, Allen, Kindle and Gladys (not their real names).  Our objective, during this meeting, was to attempt to understand their mathematical thinking.  We did this by asking students to quickly count the number of objects they were shown for a period of three seconds.  We were trying to find out how they organized the items in the picture to count them.  We noticed that each student was able to come up with the “correct” number of objects but they each grouped the items differently.

This reinforced the idea that there can be many ways to look at a problem.  Some of the students grouped the objects horizontally, while others grouped them vertically.  One student, interestingly enough, actually “borrowed” an item from a bottom row, to add to a middle row, to match the number of items in a top row.  All of the students, however, started grouping the items they saw from the left side of the page and then moved to the right side (much like reading, left to right.)  The students, however, didn’t always start at the top of the page, sometimes they started in the middle.

This experience was very eye-opening.  It wasn’t as easy to “extract” information from the students that I thought it would be.  It, at times took a lot of effort to get the student to tell me his or her thinking.  They took for granted that I “knew” what group of three they meant when he or she said, “I grouped the three objects together”.  My cohort member and I spent a lot of time repeating and pointing and circling the groupings they made. 

Another thing we noticed was that all the students added their groups of items together.  None of them noticed “x” amount of groups and then multipled that number by the number of items in  each one.  From what I could tell, the students were “adding” their groups together, rather than multiplying them.   By doing this exercise with the students, we were able to make this assessment.

Representations of Ten

Last week, while I was walking around helping the first grade students in my main placement with the math problems they had been assigned, I noticed that many of them were struggling with the “draw a picture” portion of their worksheets.

The lesson had been on determining the number of “tens” in a two digit number and the students seemed to be able to choose the correct answer from the listed choices, but then had difficulty representing it with a picture.  I puzzled over this as I heard the teacher explain to more than one student that they hadn’t finished the problem until they had drawn a picture to represent their answer.  Many of them had correctly identified that 7 “tens” were in the number 70, but they were having difficulty drawing seven towers of ten.  One student had small squares scattered across the allotted space.  Another had seven leaning towers of various heights.  Still another had drawn a tower of stacked squares, but none of them were the same size.  This puzzled me because I wasn’t sure if this was indicative of them not understanding the concept of the number of tens in a number or just of them “not being able to physically draw a picture to represent it”.    

 It seemed to me that that if the students were able to draw these groups of ten “correctly” it would help them determine their answers.  They had studied skip counting with tens and if they were able to draw distinct groups of ten they would be able to “count them” to arrive at their answer.  In my prior experience, drawing a picture had brought clarity.

Later, my master teacher and I discussed this and wondered if we should consider doing a “warm up” exercise where she’d model drawing towers of ten, giving the students step by step instructions.  Then we would give them an opportunity to practice this skill.  We had possibly moved too fast over this portion of the lesson and needed to slow down a bit, given the outcome of the assessment. 

Another idea we discussed, to see if they understood the concept of “tens,” was to have the students build the towers with manipulatives instead, rather than draw them.  Their ability (or inability) to do this would certainly shed light on their understanding of this concept.   This exercise of “troubleshooting” with my master teacher reinforced the idea that teaching math is definitely a dynamic process, an art rather than a science.  It reinforced the idea that there isn’t a “one size fits all solution” when teaching.    

Studio Day

A few weeks ago, during our Studio day in my mathematics class, I had the pleasure of meeting with two students from Maywood Hills Elementary, a second grader and a fifth grader, to talk about their mathematical thinking.   This was a very eye opening experience for me because it proved to be a lot more challenging than I originally thought it would be.  I seemed to understand the fifth grader’s thinking pretty well because he was in the Recall stage on the CGI trajectory.  He used algorithms to solve the problems from the interview task card and I was familiar with this method so we seemed to speak “the same language”.  Occasionally, I’d have to ask for clarification, but for the most part, I understood the method he was using to solve the problems.

Working, with the second grader, however, proved to be much more challenging.  I really had to listen to his strategy because I wasn’t familiar with the way in which he was solving the problems I gave him.  He, for example, when adding two, 2-digit numbers, started from the left side of the problem, with the tens, rather than the right side, with the ones.   He then represented the tens by writing lines (10-sticks) and circles to represent the ones.   After this was done, he’d count the 10-sticks and/or circles (ones) to see if he could form groups of ten.  If he did have any groups of ten, for example, ten 10-sticks, he’d draw a circle around them and write a 1-stick to the left of the tens column to represent 100. 

I later found out, toward the end of my session, that my second grade student had used base 10 blocks to learn addition.  Once I found this out many of the things he had told me started to make a lot more sense.  He, for example, had drawn a square under his circled grouping of ten 10-sticks.  I now realize this represented a 100-square from the base ten blocks.  

 I so enjoyed working with this student and once  I understood his method I was actually able to help him find a mistake he had made.  This exercise truly showed me the challenges I’ll be facing in my future classroom, to figure out the thinking of my students.

Moving From Assessment to Instruction - Reading Lesson Ideas

T enjoys reading.  He usually reads every night, at least 20 minutes.  He likes adventure/fantasy books.  Currently he’s reading a book called, Sasquatch by Roland Smith.  He told me that this book is easy for him to read but he’s enjoying it.  He wasn’t sure when he’s going to be finished reading it.  He estimated a couple of weeks (less than a month for sure).  T has good fluency when reading and uses some inflection but he doesn’t always pay close attention to the punctuation.  He often reads from one line to the next without pausing at the end of sentences and/or at commas.  He also reads very fast, but this doesn’t seem to affect his comprehension.  He a great speller, only missing one word from the spelling test I gave him during our first meeting.

T tested at the independent level on the Examiner Word Lists I gave him up through the seventh grade.  The only word he missed was desert, pronouncing it dessert.

The first reading passage from the Qualitative Reading Inventory book that I gave T was Pele.  He had never heard of him before but he knew the game of soccer very well.  He also knew what a professional athlete was.  He scored only a 67% on the concept questions for this narrative but he answered 7 of the 8 questions correctly at the end of the passage, scoring at the Independent level.  He had no miss-cues when he read this passage.   I later gave Thien two more passages to read from the Qualitative Reading Inventory book.  Overall, T seems to have pretty good comprehension when reading but I believe he would benefit from a lesson that would require him to clarify his thinking.  At times, he has difficulty articulating his ideas.  I also believe he would benefit from a lesson that would provide practice determining the most important idea an author is trying to make.          

I also believe T would benefit from a lesson on homonyms.  (He had previously confused desert with dessert).  The teacher may want to try dividing his students into two teams where a representative from each one take his or her place at the board in the front of the classroom as the teacher challenges them to write sentences using words that have more than one spelling and/or meaning (For example; Our principal was really testing the teacher’s principles.)  The two teams would compete with one another.  Having the students play a game would make this activity both fun and educational. 

Reflection on peer blog responses to my Writing Analysis

The feedback I received from my writing group was constructive, specific and timely.  Brian mentioned that I might want to consider incorporating technology into my lesson.  In response to this suggestion I found a great online crossword puzzle activity dealing with synonyms (for the words good, nice and bad).  I could possibly use this as an extension activity or possibly assign it as homework.  This site would provide a fun and interactive way for students to get additional practice finding synonyms. 

Brian also mentioned that I might want to have my students draw a picture, based on the descriptions written by others in the class.   This would show the students if their writing was providing enough detail by the drawings produced.   This would also work well as an add-on activity. 

Thirdly, Brian mentioned that I might want to provide some instruction on how to use a thesaurus before expecting my students to use one.  This suggestion reminded me of the importance of not just assuming my students know how to do something. 

Jessica also provided some important suggestions.  She indicated the importance of ensuring that my lesson follows the “gradual release of responsibility” model to optimize student learning. Explicitly thinking and writing about these stages helped clarify my lesson.   (I had followed this model in my write- up but hadn’t explicitly included this type of language.)

Lastly, Jody commented on the importance of this lesson (of finding synonyms) and suggested that this type of lesson be done frequently.  We both agree that teaching students to add meaningful descriptions and details in their writing is an important skill to learn.

An Engaging Mathematical Environment

My mathematics methods class this quarter has prompted my thinking about the many ways in which math is taught and the importance of creating an environment that promotes learning among students.   I now realize that the teacher in my dyad placement last quarter, a fifth grade classroom at Einstein Elementary, was extremely successful at creating just such an environment.  Every student seemed to be engaged in the lessons he taught.  As an “observer” I wasn’t able to guess which students seemed more challenged by this subject than others.  They all actively participated.    Now that I’ve begun reflecting more on his teaching methods, however,   I  realize that he incorporated  many important  strategies into his classroom that  helped create this amazing “mathematical environment” (that I, of course, hope to replicate in my own classroom some day).  This blog is devoted to sharing some of these strategies.

One of the first things I noticed about his classroom was the level of attentiveness of his students.  Everyone was facing forward and quiet while he was speaking during his lesson.  They were also quiet and respectful when other classmates were speaking.  When I asked him about this he told me that he had established the rule early on that no one should talk over anyone else.  I later realized that this behavior didn’t happen by chance.  He would abruptly stop, mid-sentence, and look directly at an offending student if they were talking out of turn and would not begin speaking again until they were quiet.  This method was extremely effective.  It reinforced the message that each member of the classroom had something valuable to contribute and, therefore, should be listened to.   

Another effective strategy he used was his warm-up activity.  He always had the students play a math game that related to the lesson he would be teaching.  He usually asked for a student volunteer to come up to the document camera to play the first round with him, as he explained the rules, before handing out the game pieces and “boards” (papers) to play.  This seemed to generate excitement among his students.  The class would then be broken up into partner groups to play on their own.  During this center activity part of his lesson, when the students were in these table groups playing the math game, the teacher often called out a group that was on task.   This reinforced the expectation that all students were to stay focused on the game and not get sidetracked in conversions about anything other than math.  He also did this during student independent work time.  These “gentle” reminders seemed to keep his students on the right track.    

This teacher also taught very engaging lessons by using just the right mix of direct instruction and student involvement by asking students to volunteer to solve problems on the active board that reinforced the concepts he was teaching.   He was also adept at keeping the lesson moving at a comfortable pace by often checking in verbally with his students by asking them if they understood how he got a particular answer to an equation.  He’d ask for a “thumbs up,” close to their heart (so only he could see) if they understood.  If he didn’t see many thumbs he’d review the problem again.  This enabled him to “slow down” if necessary, but also to “skip forward” if the concept was understood by all.

He also had great strategies for involving all of his students.  When he asked questions about a solution to a problem he’d often wait until most hands were up before continuing on, and then he’d ask them to form partner groups to discuss the answer (instead of just asking one person to give it).  This method of student involvement was discussed in the Questioning Your Way article, by Mewborn (that was assigned reading in my class).  Per the article, “By sharing their solutions in pairs first, students can try out their ideas on someone else and practice what they are going to say to the class.  Students receive feedback on their solutions in a non-threatening setting, and their self-confidence is boosted.”  This seemed to be true as I witnessed this practice in my dyad placement classroom.  I noticed the “hands” of students that didn’t typically participate to offer a solution when the teacher brought the class back to attention.

This teacher was also very respectful of his students when handling “wrong” answers by calling on others to assist the student having trouble, so they could eventually be successful.  (A student that made a mistake on the active board was never permitted to return to his or her seat until they had successfully completed the problem.).  Another part of his lessons that I especially liked was when the teacher purposely made a mistake when solving a problem, and then asked for volunteers to find his “oops”.  (By doing this he kept the lesson light hearted.) He would also, on occasion, take on the entire class as his opponent during a math game to spur competition among his students.   They seemed to be especially involved and engaged during a lesson when they had the opportunity to “beat” their teacher.

I truly enjoyed observing these math lessons during my dyad placement.  This teacher modeled many of the strategies we’d been discussing in my mathematics classes.  I was able to watch as he put many of these effective strategies to practice in his classroom.