Conceptual understandings require time.

In order for students to reach deep and conceptual understandings they require time. Time to explore concepts, time to think, time to build connections.    I regularly use the thinking routines by Project Zero, which are designed to:

“Slow down the pace of the classroom to make space for deep observation and wonderment.  That happens by talking and discussing objects or systems in the everyday world.” (Schwarz, 2014)

There is great value in slowing down the pace of the classroom in order to reach deeper and more conceptual understandings.  A common misconception is “We don’t have time, we have so much to cover!”.  But by teaching and learning in a more thoughtful and slower way, you actually save time in the end.  By establishing solid understandings you are eradicating misconceptions, which you would have had to re-address later on, had you just rushed through.

I want to highlight this point with an example of my students learning about TIME and how to ‘tell the time’ in our current UOI.  The line of inquiry which we are exploring is “How people organise and measure time”.

Telling time is often taught as a rote skill and with this comes deep misconceptions.

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Traditionally, teachers often start with teaching the full hours “When the big hand points to 12 and the little hand points to 1, it is  1 o clock”.  Then onto half past 2 and then onto  quarter past and quarter to the hour.   But when our students learn time in this way, they do not have an understand of “the duration of time and its relation to the numbers and hands on a clock” (Thompson and Van de Walle 1981), nor do they have a true conceptual understanding of time.

Before designing my lessons on telling the time, I did some research.  And, no, I did not consult Pinterest, instead I went on the National Council of Teachers of Mathematics website http://www.nctm.org/ and within 5 minutes I had a series of investigations designed to:

“provide opportunities for children to investigate time units, experience events lasting set amounts of time, and develop personal referents for standard time units” (Mc Millen and Hernandez, 2008).

These investigations by Mc Millen and Hernandez (2008) were different to other approaches I had read and observed,  these researchers  highlighted the differences associated with the two hands of an analog clock and why these two systems should be taught separately at first. In these investigations  students worked with two types of one-handed clocks, a minute clock and an hour clock, to meaningfully discover both differences and connections between the two clock hands.

By spending a little amount of time doing some research, I saved myself a lot of time in planning.

In the first lesson, I gave my students time to investigate time units such as 1 second and 1 minute, in order to help them to develop personal references for standard time units and to discover the relationship between them.   My classroom was loud and noisy.  We were building towers, bouncing balls, doing star jumps, burps and … you name it!

 

In the second lesson, the students investigated what can be determined about time when a clock has only an hour hand.   We built our own clocks and learnt how to tell the time with these simple phrases, its “o’clock” its “a little past five.” or “a little before five o’clock.” or its  “between four o’clock and five o’clock”.  The students worked in partners and had a number of partner activities to do, which they greatly enjoyed.

In the third lesson,  the students then investigated clocks with only a minute hand.  This lesson focused on connecting  minutes to an hour.  We started by matching ‘groups of five minutes’ to the clock face and built minute clocks in our classrooms.  I encouraged my students to use efficient counting strategies to tell time, eg, skip counting by 5s: 5, 10, 15, 20, then counting on individual minutes 21, 22.  By the end of the lesson, all my students were all able to count the minutes past the start of an hour with their partners.

In the fourth lesson, my students  “investigated the motion and location of the minute hand as it relates to the hour hand” (Mc Millen and Hernandez, 2008).  My students then connected their knowledge together, they counted the minutes first, then found the hour, and finally combined them.    At this point I exposed my students to analogue clocks with both hands, and after some discussions “Which comes first, the hour or the minute?” My students were all quizzing each other “Guess which time this is?” and telling the time to the minute.

It took 3 lessons (4 hours in total) before I even introduced my students to a real clock face with two analogue hands.  Yet, my students were able by the end of that 4th lesson to tell the time accurately and to the minute.  This is my 4th year as a Grade 2 teacher, and never yet have I seen students learn the time faster.

What can I conclude from this experience?

It pays to give students time, time to understand concepts deeply and in the end, well … you might even save time.

If you are interested in any of the sources mentioned here, they are referenced below.

McMillen, S and  Hernandez, B (2008) Taking Time to Understand Telling Time.  The National Council of Teachers of Mathematics. accessible at http://maccss.ncdpi.wikispaces.net/file/view/Taking+Time+to+Understand+Time.pdf

Schwatrz, K. (2014) How Dissecting a Pencil Can Ignite Curiosity and Wonderment. MindShift. accessible at http://ww2.kqed.org/mindshift/2014/12/08/how-dissecting-a-pencil-can-ignite-curiosity-and-wonderment/

Thompson, C and Van de Walle, J (1981). A SingleHanded Approach to Telling Time. Arithmetic Teacher 28 (April 1981): 4–9.  cited in McMillen, S and  Hernandez, B (2008) .

 

 

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