Shallow understanding of mathematics

Today I try this journal prompt with my students. Write a word problem with the answer as 5x.

As this is the first time the students are doing it, I try to give them an example with the algebraic expressing (x+5). Explain to them now we are “doing the opposite”. Usually, you are to solve the problem. Now , you are to create a problem with the answers provided.

Sensing that the students are at a loss as to what to do, I decide to provide them with scaffolding by giving them some key words to use. They can either use “each” or “as much as”.  I would have though that these keywords are a “give away” but I am proven very wrong.

Looking at their journal entries, only about half of them seem to know how to create word problem. From their entries,  it seems that they do not have a deep understanding the use of “each” and “as much as”.  They may seem able to solve the word problem but they might be just doing mechanically without any real understanding (e.g., see “each” and “as many as”, just times …)

I can see their shallow understanding in solving geometry word problems. In getting them to articulate the property used, they would just say “angles in a straight line” when they see 180.

From these various episodes, it appears that my students are simply “hatuming” .  They are not thinking deep enough. How to make them think “deep deep”? Here are some of the activities that I can think of :

(1) Get them to look at their friend problem and identify the mistake

(2) Modelling the problem-solving process. I need to show them how I try to understand the word problem through a series of questioning.

(3) Make them verbalize their problem solving process (e.g., using screencasting)

There is lots of work to be done but I will continue to strive on. Why? Because they are my students and I would always do what I can for them.

 

Activities, Activities and more activities

Looking at my science lessons for the past one week, it has indeed been very action packed.For the P6s, I have used toys to introduce energy (E.g., elastic potential energy in spring and rubber band , use of hand generator to “see” energy conversion) . For P5s, they are setting up circuits to experience the electrifying electricity. Such  activities can possibly help them to enhance students’ learning and memory.  When revisiting/reviewing the concept, I can refer back to their  activities-doing to extend their existing schema

 

These activity-based lessons allow the students to be doing-thinking But , the challenging point is how to get them to think about their doing. I find myself walking around and asking them questions. Or, I will stop the lessons at the mid point to bring their attention to what they should be thinking.

But, does these activities really work as planned? Well, one of the standard answer you will hear is that the students are engaged. But, what are they engaged with? Perhaps with just the doing only..

 

The challenge for me is how to get them to think-do especially for my P5s. I personally that it is a habit that they must cultivate. For my P5s, I try to get them enculturated in this type of thinking-doing. Looking at what they have written in the textbook, it seems that they are mostly doing and not just thinking about what they are doing.  They might be too engrossed in their doing that they “anyhowly” complete the workbook when it is time to hand up their book. In order to get them to think-more, here are what I would do or continue doing:

(1) Get them to articulate what they are doing (while walking around or classroom discussion)

(2) Make it a routine for them to complete the designated exercises in their WB before allowing to explore

(3) Get them to blog/write about their doing.

So, how about my P6s who are not strong in science ? I would do similar things but perhaps give them more scaffolding (like helping words and modelling the thinking).  I notice that they are quite hesitant as I ask them questions about their doing. They do not seem confident of their answers even though their answers might be right. Is that a matter of learned helplessness? Perhaps… I guess I need to ask and encourage them more to give their answers.

 

 

 

See something, say something

See something, say something.  How many of us do have the moral courage to do that especially in the face of higher authority?

So, what about me ?

I guess if it is worthwhile for me to say it, I will say it . There is no stopping of me as things meant to be said has the  be said.  Of course, there are risks. But, if I choose to say something, I do it  with my eyes wide opened , knowing all the possible consequences.  In simple term, I do it with eyes open and willing to take any consequences (may it be good or bad) that comes with it . If I am ‘defeated’, I won’t blame others but rather than my inability to hold my ground.

Yes, currently, I am very angry over something and I am waiting for the opportunity to say something in the most appropriate time.  I don’t care if I am ‘killed’ along the way for I just need to make sure I am not part of the problem. Not willing to speak up is part of the problem and I refuse (I repeat, simply refuse) to be part of the problem.

I am just waiting for the right time and I shall move in for the ‘kill’.

Teaching algebra

It is my second year teaching P6 Standard Maths and second year teaching algebra. Compared to last year, I feel that I am more explicit and clear in my teaching. I am mindful of the use of terms and always try to make the meaning of the terms explicit. For example,

(1) Meaning of the variable : Represent unknown number

(2) 3x : Instead of saying 3x, I always says 3 groups of x

(3) 3+x : You cannot add a know number to an unknown number

(4) Use of model to represent algebraic expression

Even getting the students’ response, I also make sure that they also articulate the meaning of the terms.  Unlike last year,  I did not try to teach them “mechanically” but rather trying to get them to articulate the meaning.

How is that going? So far, they seem to catch on (at least during the class activities). Let’ see how that translate to their actual test. I am simply keeping my fingers crossed.

 

 

 

Same Same but different [P6 E-experiment , 2nd year]

This year, I am going to do the e-experiment with my P6s again after last year experience [Link]. I have included the data validation in the form after reading the responses from my colleagues’ who had done the experiment last Friday. On seeing their responses (like including mm in their answer and giving more than one response), I suddenly remembered that my little rascals also made the same mistakes last year. Guess it slipped my mind as I did not blog it down. I should have put in the data validation in the form in the very first place. It is an oversight on my part.

As the remaining three classes have not done the experiment yet, I quickly put in the data validation in the Google Form. To find out how to use the data validation, check out this link

Have tried the experiment 2nd time. For this year, I gave more detailed instructions due to the nature of the class. This included:

(1) What does the bubbles contain?

(2) What do we need to measure the number of bubbles?

(3) Giving them the distances and make sure that that they recorded on their activity book.

I then ended off the lesson by highlighting two ways to test for photosytnthesis :  (1) Number of bubbles (2) Testing for starch

Some interesting observations:

(1) Some students does not know how to count “1 minute” .  They think that 1 minute is up when the clock hand reaches 1.

(2) Students knew that the answers must be more or less the same. I heard some conversation that “your answer is not close to mine”. Good to teach them about reliability.

My reflection

I think it is important for the kids to experience this simple experiment.At least, they  are “doing” the experiment. Whenever I review photosynthesis with them, I can also say, “Do you remember the experiment we are doing in the computer lab? ” What is that all about”? By referring to this “doing”, hopefully, they can remember the facts about photosynthesis better!

This e-experiment serves a different purpose from my last year class. For my class last year, I want them to experience what a scientist do. Same experiment, different purpose.

Gap, Gaps and more Gaps!

As I reflect on what happens in the first two weeks of the school, I realize that I am more aware of students’ responses and try to build on them. I am trying to address the students’ gaps  based on their responses. Here are the responses that I have received so far and how that influence my next step :

(1) Students’ not too good at mathematics fluency as articulated in the previous blog post [Link]

(2) Students’ alternative concept with 3+y and 3y (From the Nearpod)

(3) Not able to recall the photosythesis (Through journal entries in biology textbook and MCQ in Activity book)

(4) Not able to use “electrifying” terms (Through journal entries in biology). Observations from the journal entry:

– Just simply using conductors and insulators. Do not talk about the current flow in the description.

– Talk about the topic generally, without applying to the context.

One of the kneejack reaction to all this is to teach more!! Just tell the students and you expect them to remember. I guess I am not going to do so much of that but rather design learning activities to get them the make their thinking visible.  These are the activities that I have planned for Week 3:

(1) Maths Journal Entry : Get them to articulate the “why”  in the “commonly wrong” fundamental maths problems. This include journal prompts like Which number is bigger : 1.6 or 1.09 ? Explain your answer

(2) The problem with 3x and 3+x . Will likely to get them to screen cast the working and get them to talk about it.

(3) Science Blogging : Getting them to write a letter describing what they have learned about electricity for the past two weeks. As a follow up activity, I will get them to peer critique the students’ posting withe the success criteria provided.

(4) Get the kids to create a mnemonic to remember the facts.

 

Adapting to warmer seas!

Another article caught my attention in the Straits Time today:

“Corals adapting to warming seas”.

This article is relevant for the following topics:

(1) Adaptions of Corals: How does the coral adapt to the increasing temperature?

(2) How does micro algae adapt to the increasing temperature?

It is getting absurd.

All I can say that certain thing is getting absurd  and the absurdity has taken on  a new level today.  Why? Contradictions in the loads of statements given.  For example, , documents are not meant to be read deeply. I go like “huh”. Then, why strong words like “comply” and “must” appear in the document?

If I chose to be very aggressive, I would focus on one of the smokey statement and would not let go. But , I choose not to. I do not want to stoop to that level. No point saying more as the other other party is obviously not listening. I have said my piece and I stand by what I said.

I know that I am stepping toes by making my opinion known in an open meeting like that. I need to do it because if I do not speak up, I would be part of the problem too. I am glad that I have done it and hope more will speak up and ask questions.

All these are  definitely making me very angry and make me all the more to fight back against the absurdity of things ! Idc if you are not feeling well

Why? Because I  need to stay true to my conscience.  I need to do what is necessary and right not not do things because I am told to follow to the dot. Period.

To hell with that absurdity.

PS: No one should ever say that I *short change* my students. I never did. And that absurd statement really pissed me off.

Mathematics fluency (a 10 minute exercise that reveals my students’ learning gap)

For the past one week, my students would have mathematics fluency exercise at the start of the lessons. I have tried to vary the exercises, from using (1) two dices for them to form number statement (using the animation at : http://a.teall.info/dice/ )   (2) Socratic App (3) What makes 8?

This simple 10-minute exercise reveal the students’ learning gaps in fundamental mathematics fluency. This includes

(1) Not able to tell which number is bigger : 1.09 and 1.9

(2) Not able to covert improper fraction to fraction

(3) Having difficulty in identifying the digit in the tenth, hundredth place.

(4) Not fluent in multiplication facts.

Well, this shows that there is lots to be done to close the learning gaps. I will try to cover the fundamentals (e.g., place values before I go on to more complex stuff).

Am I daunted ? No! My last year’s experience with my beloved  rascals last year  has made me feel “zen” with such learning gap.  I will enthuse this group of students like what I did last year. I will pull no stops to make them step up before the upcoming PSLE!

 

 

Voting for the class council

I allow my class to vote for their class council this year.I only told them on Thursday and made the “candidates” said a speech after lunch.  I told them that both we would totally respect their choices for at least a month and would see who they had chosen if they indeed were fitting for the role.

I had five students volunteering for the posts . I shall say I am petty impressed with their speech. Most of them were willing to share their weakness and wanted to change for the better. I shall say this was a “emotionally-intense” election with candidates “breaking down” due to their low votes.

The best part ?? The students “run the elections” and I just sit back and videotaped down the speech. I only needed to count the votes to ensure impartiality. I am letting go the control of the class and it was good how they self-organized (e.g., getting the candidates to speak and encouraging and supporting the  candidates). Some candidate was upset over their no-win and their peers, on their own accord, comforted them.

Some learnable moments from this election

  • Students would need to live with their choice for at least a month as they need to be responsible with the choice they made
  • Some candidate was upset due to the low vote and I encouraged the kids to take setback in stride.
  • The votes were close and I urged them to respect the class’ choice and the class shall stay united. (Think the recent #brexit and #trumpwin)

They have made their choice and I would see how that would turn out in the month to come.

PS: It does not take one month . Feedback from other teachers has made up expedite our decision to change the HC and AHC. I broke the news to them and surprising, they took it quite well. Perhaps, they were self-aware and felt that they were indeed not suitable for the job. Of course, we assign them other roles for them.