Kindergarten, Counting and Cardinality 2/3

Opinion – How to fight back against the invasion.

COVID-19 has invaded our planet. It’s making some people very sick and killing some of the most vulnerable. It’s almost time for children to return to school in the USA, but parents and teachers are afraid. Their fears are real because we are fighting the virus with too few tests, too little ability to trace contacts, and no vaccine.

So, what do we do? It may be true that the children themselves are at low risk – the data are not yet conclusive on this point – but as with other flu bugs, children are quite capable of bringing the virus home. At a minimum, to send our children off to schools and indoor classrooms, we need reassurance that health guidelines – masks, daily testing, distancing, ventilation, time limits, hand washing, etc. – will be followed. Moreover, we need some confidence that schools are actually equipped to implement those guidelines. However, some level of risk will remain and any breakout at your school could lead to a shutdown. The probability is rising that your child will receive online instruction during the next year or two. Are her teachers ready to deliver that instruction effectively? Do you and the school have the technology you need to support that plan?

Any way we look at it, real learning is likely to suffer. So how do we prepare for the drought? If there is no water on our hiking trail, we must plan ahead to be safe; we must carry our own water. If schools are unlikely to reopen soon or to connect effectively with our children online, home-schooling is one option, but it’s not right for everyone for various reasons. Some charter schools, because they operate under different constraints, have shown themselves to be effective distance-teachers – I leave that research to you. It appears to me that at a minimum, you should consider stepping up, at least in the area of math, as your child’s coach.

Make sense? Let’s continue our journey; we’ve only just begun.

CCM Lesson of the Day: Counting and Cardinality (K.CC), 1/3/2

Count to tell the number of objects.

Understand the relationship between numbers and quantities; connect counting to cardinality.

When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

Opinion: That’s a lot of words to describe counting. My suggestion: just count stuff. Count fingers, toes, apples, Cheerios, … Then ask, “how many?” Count numbers. That’s right, count 1, 2, 3, 4, 5. If I do that, no matter where I stop, I have counted that many numbers, 5 in this case. This will help to relate the symbols to the words and to illustrate cardinality (see the definition above).

Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

Comment: Your child will get this. Count the fingers of one hand from small finger to thumb. Then count them from thumb to small finger. Any bets on the results?

Understand that each successive number name refers to a quantity that is one larger.

Comment: Fingers can be useful here too. As we count, we can interject “plus one.” “One plus one is two; two plus one is three; three plus one is four.” This sets the stage for addition.

Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Comment: Sure, ask your child how many apples are in the bowl. Then, ask your child to give you three apples. This will provide a head start on comparing.

Definitions

Ordinality: A number indicating position in a series. For example, consider the series of characters {a, b, c, d, e, f, g, h, i}. The cardinality (feel free to revisit the definition from the previous post) of the series is 9. The ordinality of the letter ‘f’ is 6. Why, you may ask, is this important for kindergartners; actually, I don’t think it is. However, as a parent, you need to understand CCM language. But wait, you didn’t even see the word ordinality above; very true, but if we’re going to discuss cardinality, we really should mention the complementary term, ordinality.

Plus: Plus indicates addition, as in 2 plus 1 is 3. Admittedly, I introduced this term for convenience, but we will need it later any way.

How many? What is the number of objects in a set, as in the number of apples in a bowl? This is just one more example of your child learning English at the same time he is learning math.