Teaching Multiplication… much more than “Shoot Out!”
I am not a fan of fast fact math games like ‘sheriff” or ‘shoot out’ and it doesn’t help teach students about multiplication! There I have said that out loud! There seems to be a misguided notion from students and some teachers and parents that speed in the recall of facts defines your capabilities and ability as a math’s person…I have come across many people who think that if you are fast at fact recall then you’re good at math. Well let’s set the record straight… this is NOT TRUE! And I am on a mission to change this terrible point of view with parents, students and teachers alike…
The first sign that someone thinks speed is an indicator of a math ability are seemingly “FUN” games that focus on the fast recall of facts. These pressure situations actually do more harm than good, especially for levels of confidence, risk-taking and Growth Mindset, and need to be approached with caution and timed just right! These games only build speed in the recall of the facts that the students already know, they do not help them with the facts they don’t know neither does it build any understanding of the multiplication concept. In fact students who only know facts and who have been rushed into recall before developing understanding, probably wouldn’t know a real life multiplication task if it was right under their nose!
Banish Math Anxiety
And what about the slower, less confident student? They may actually know the answer but can’t perform due to huge amounts of stress and anxiety. For these students such activities don’t help their learning but facilitate math anxiety and stress, and the feeling that they are not good at maths, it may even make them HATE maths! So what is the answer? Yes students do need recall and speed, but this is something that is developed after exploring and investigating the multiplication process and over time with practise, but please don’t write a student off as ‘not good at maths’ because they can’t recall with speed, I still cannot recall 7 x 8, to this day, without saying in my head 6 x 8 is 48 so 7 x 8 is 56 !
Strategies Over Speed!
For students to solve multiplication problems they need to understand & own multiplication knowledge which takes lots of investigation and exploration in many different contexts. But before this can happen it’s important to identify what the needs of the students are. So how would you do this? a test right… well actually no! Depending on the test that you do and based on most regular textbook tests for multiplication, it may only show crosses and ticks and not what the students understand about multiplication. So the right type of assessment is needed, and it needs to identify what the student can do as well as what they can’t do so an appropriate level of differentiation can be added to the maths program. This is a difficult thing to achieve but by using the right type of questioning in your teaching, you can start to see what student’s can and can’t do, and specifically where their understanding breaks down. This is where the work of Dr. Anne Newman comes in and the use of Newman’s analysis.
All too often it is assumed that students who see the problem 3 x 4 automatically read it and know what they must do to solve it. How ever, what usually happens is that the students have been told, often inadvertently, that they are ‘learning multiplication’ so they have been told to do multiplication to solve problems! If we take a different approach and follow Newman’s prompts and questions during interactions with students then we will be able to analyse the levels of understanding students are using and where it breaks down, and so plan curriculum to ‘fix’ areas of need!
Newman’s Prompts & Analysis
Australian educator Dr Anne Newman’s research (1977) into successful problem solving found that students progress through 5 hurdles during problem solving. Try these prompts, from the perspective of your students to solve the multiplication problem 3 x 4 = ?Read More & Watch Our Video About Newman’s Prompts Here…
We have put together a simple cheat sheet with these prompts so you can have them at your fingertips >>> CLICK Here To Download your FREE Newman’s Prompts / Analysis Sheet
Our Favourite Children’s Books With A Multiplication Theme
So now onto a range of Multiplication Strategies that will help build multiplication understanding. Here are 5 of them: Repeated Addition, Equal Groups, Skip Counting, Arrays, Commutative Property.
Check out our Multiplication Pack for Activities, Thinkboards & Classroom Posters for these concepts.
Repeated addition is the easiest way to solve multiplication problems but it requires students to be able to interpret a multiplication problem correctly. For example the problem 3 x 4 would be 3 added together 4 times. Start by using materials, pictures and then a number sentence to help students make the connection 3 x 4 is actually 4 + 4 + 4 explain why it’s not 3 + 4 or 4 + 4+ 4 or 3 – 4.
This is the first step when introducing multiplication to your students. so using 3 x 4 as our number problem students would be taught to interpret this as 3 groups of 4 and represent it with concrete materials then drawings.
Is a more efficient way of counting a collection that links to multiplication. It is helpful for students to match a chant that they have memorised to physically moving and counting materials to help them make connections between the chant and counting.
Arrays are useful models to link repeated addition, groups of & skip counting together as a way of performing multiplication. Use objects, stickers or dots arranged in columns and rows. Each column must have the same number of objects as the other columns. It is an efficient way of ordering materials to count and by adding another column each time students can see the multiplication facts growing progressively. This model helps build a visual image to aid memorisation.
The Commutative Property is a great way of cutting learning multiplication (and addition) facts in half. This property applies to the order in which computation is carried out and highlights that changing the order in which digits are multiplied, will not change the answer so 3 x 4 = 12 and so does 4 x 3
Multiplication Fact Mini Book
Here’s a little multiplication booklet that your students can make to help them with multiplication fact fluency.
Italian Lattice Multiplication dates from 1478! … Click To Watch The video. An alternative written multiplication strategy introduced by Fibonacci . This strategy utilises partitioning & the distributive law to solve multiplication problems. Wish someone had shown me this. CLICK FOR FREEBIE