Cutting the curriculum - Grade 1 Math

I’m writing a series of blog posts to highlight that the primary curriculum is overloaded with content. With pressure to cover this content, teachers are unable to give the less able children the help they need and they get left behind. I welcome comments and feedback on these posts, especially from teachers who have developed methods to overcome the hurdles I have described. I confess that math teaching isn’t my forte.

Mathematics must be the most challenging subject to teach, if one is aiming to ensure that all the children in the class reach the level of numeracy of which they are capable. There is such a wide range of ability among children –  several years above or below the average in a given class. In a grade 1 class there could even be children at Piaget’s stage 1. They can count in the sense that they can recite the numbers in order, but not in the sense that they can count objects. Young children, when they are learning to count, are liable to move more than one object when saying one number name. They also say that there are more in a set of objects when they are spread out than when they are close together. No amount of telling them will convince them otherwise.

However, there comes a point in their mental development when they are said to conserve number – they understand that the quantity doesn’t change if it is rearranged. At this point, and not before, they are ready for the concept of addition. So, in a grade 1 class, there could be some of these children, and others, probably the majority, who already conserve number. This presents a dilemma. Ways need to be found to help the stage 1 children, by presenting them with a variety of situations requiring counting, without making them feel that they are failures. They need to find what they are doing is fun and interesting to build up their confidence and motivate them to persevere. That is not to say that the majority of the children are ready to race through the curriculum at breakneck speed, only that there are some children who are not ready.

Now to look at the curriculum, for Grade 1, Term 1, taken from Mathematics Scope and Sequence Grades 1-3, August 2016 Version 5  (in blue. My comments in black.)

September

Number strand

a.    Identify numbers 0-10.

b.    Identify set with up to 19 members

c.    Place number 1–10 in serial order

d.    Use objects to create sets 

e.    Identify objects which belong/do not belong in a set.

f.     Count the number of objects in a set

g.    Matching members of a set- same/fewer/more..

h.    Compare sets.

i.      Partition 2-10 members in two or more sets.

j.    Identify whole set.

k.  Identify parts of a set.

l.    Identify the empty set.

Geometry strand

a.   Identify geometric shapes in natural and man-made objects (eg. natural objects: tree, man, hill, sun       

     manmade shapes: roof, window, ruler, ball, book 

Is it realistic to expect  to cover all these topics in September, when the children are settling in to a new school, and teacher and students are getting to know each other? Teachers are expected to review each previous lesson before presenting each day’s topic. What if the review reveals that re-teaching is necessary? Also, children in grade 1 need plenty of practice in writing neatly in exercise books or workbooks and forming their numerals.

October

Number strand

a.   Use Ordinals up to 10^th.

b.   Write number words 0-19. Why are numbers above 10 being introduced so early?

c.   Write numerals 0-19.

d.   Associate number with numerals.

e.   Identify set with 20 through 100 members. Grade 1 children have little or no concept numbers 20 – 100. Are they expected to count 100 objects before learning about place value?

f.    Join two sets (up to 10 members) using mathematical sentences.

g.   Use +, -, and = correctly to complete mathematical sentences.

Measurement strand

a.  Identify measurable attributes of objects for eg. A box  has dimensions (length, width, height), weight, volume (non-standard)

b.  Use comparison and describe objects using

o   long/short

o   wide/narrow

o   thick/thin

o   heavy/light

o   large/small

o   tall/short (use concrete, semi concrete and  then abstract to do the comparisons)

c.  Identify objects of equal/unequal length.

d.  Estimate and measure

the length of various objects using non-standard units           . (for eg. Hand span, foot prints, fudge sticks, finger width, paces, connecting cubes, paper clips)

Geometry strand

Use any simple shape to   make pattern by repetition (e.g. Ink blobbing, tessellation, potato-printing)

Again, there is too much for one month.

November

Number strand

a.    Know ‘one more than’ facts. Many examples of these can be given, such as how old they will be next year.

b.    Recognize and make ten facts

c.    Memorize and recall addition facts up to the sum of ten. I’m sure I can’t be reading or understanding this correctly. Do they really mean that the children should know all the addition facts for all the numbers 1 to 10? There are 45 such addition facts!

In “Mathematics we Need” (the text used in Jamaican schools in the 80’s) grade 3 students were learning the addition facts for the number 7. I am very much in favour of children learning addition facts, (too many children are counting on their fingers in later  grades), but they need more time to get a feel of a number before  learning its addition facts.  For example, for the number five, they can know ‘fiveness’ in relation to an arrangement of dots; to the subsets of five in pictures on a page; in counters which can be  moved around; in units of measurement and in ordinal numbers. I would suggest that addition facts up the sum of 5 is the highest number they need to learn at this point.

There is an app called “Calculation Time” which uses dominoes (without the 6) to help students with mental arithmetic. Some, but not necessarily all, students will love it and learn from it. Furthermore, as yet not all students have access to this app.

d.    Know addition facts (commutative property). This should be taught before “c”.

e.    Associate the addition of up to three numbers with the joining of sets.

f.     Adding zero to any number.

g.    Use +, -, =, ≠, correctly to complete mathematical sentences.

Measurement Strand

a.    Use concrete materials to investigate the relationship between the size of a unit and the number of units needed to measure length. E.g. compare the number of paper clips and pencils needed to measure the length of a table.

b.    compare and order objects by their linear measurements using the same non-standard units. E.g. using a length of string equal to the length of your forearm, work with a partner to find other objects that are about the same length.

Geometry strand

a.    Identify straight and curve path and associate them with longer and shorter paths.

December

Number strand

a.    Identify greatest or least of a set of numbers. (0 – 19)

b.    Compare numbers: greatest/least.

c.    Use +, -, = correctly to complete mathematical sentences.

Measurement Strand

a.  Identify days of the week and months of the year.

b.  Use a calendar to calculate days and weeks for specific events.

c.  Tell time on the hour,   half an hour on a digital and analog clock.           

d.  Show time given orally on the clock face.

e.  Associate time on the hour or half hour with daily events.

f.   Use estimation to compare times spent on various activities.

g.  Associate months with school activities and holidays.

There are fewer teaching hours December, because of end-of-term review and tests, Christmas activities and Christmas holidays, so there's not much time to introduce new material. Most of the activities in the measurement strand are covered from time to time in the Integrated Studies Curriculum.  Furthermore they don’t need to learn the half hours until grade 2.

Any changes in the first term of grade 1 will set back terms 2 and 3, and ultimately the ensuing years, but unless a solid foundation is laid in Grade 1, children will struggle in later grades or give up completely. We should try to make math interesting and fun for all children so that they continue to be motivated.
I think this curriculum was implemented in 2017. It's worth noting that performance in the Grade 4 Numeracy Test has been showing steady improvement from 53% mastery in 2012 to 74% in 2018, so something good must have been happening in grade 1 classes between 2009 and 2015 before the introduction of this curriculum. Perhaps we should try to identify what that was.
In a subsequent blog post, I will compare grades 6 and 7 curriculum, where there is a great deal of overlap, to show that many of the topics in the grade 6 curriculum can in fact be left until grade 7.