Connecting to maths language...

'Imagine a teacher running her hands across her desk as she tells her students, “A plane is a perfectly flat surface.” The students listen quietly, but one of them is thinking, “I thought a plane was something that flies.' Rubenstein and Thompson, 'Understanding and Supporting Children’s Mathematical Vocabulary Development' (p107, 2002). 

This is the type challenge many of my learners face everyday. Donna Yates shared this article with me after visiting LS2, along with a great idea to help us strengthen our connections to the maths language we encounter when reading and trying to make sense of written maths questions. Rather than reinventing the wheel I used this exact example to show my learners how confusing maths language can be, and gave us an authentic purpose the challenge that followed.

I find that when my learners collaborate and have the opportunity to talk about their tasks they gain a clearer understanding, so this is how we approached this challenge. There was a lot of negotiation and rich discussion as the vocabulary was manipulated into the corresponding columns. Donna is happy for me to share the link to this task which can be found here.

Going forward I will be tapping into the TESOL strategy of repetition without boring. If I want my learners to forge strong connections with the vocabulary they need to be successful in maths I know I need to provide multiple opportunities for these students to hear the words, see the words and use the words in context.

Inference: When do we use it in our learning?...

Having unpacked and explored the comprehension strategy of inference during reading lessons I wanted my target students to be able to tap into this learning and use their inferencing skills during our maths lesson. As a scaffold for these students I asked my whole class to remind me of when we use inferencing skills in our learning. What completely shocked me was that not one person could answer this question. Incase there was a confusion between inferencing and inference I asked my students what inference was. Again no one could give me an answer! I used a variety of DATS (direct acts of teaching) to prompt a response but still no one gave me a correct response. Thinking on my feet, I recited the nursery rhyme, Jack and Jill then asked my learners two questions. 

1. Was Jack a boy or a girl? 
2. How old was Jack? 

When the answers were given I asked, 'How do you know?' I was told that Jack is a boy's name so we can assume he's a boy, and he's young because in all the books they have a little kid drawn. I then cast a written version to the TV and asked everyone to talk to their buddy and show them where this information was in the text. One student said 'We can't Miss because it's not there.' I then explained it isn't written in the text because there are enough clues in the words (and images) for us to logically guess this information. 

I think my learners were thrown by my question because we always talk about inference and respond to inferential questions during our guided reading sessions, but on this occasion I asked them a reading based question during our maths learning time. Unfortunately none of my learners were able to knowingly transfer learning from one context to another. 

We then looked at the maths question: 

197 adults and 152 children were on the afternoon flight from Christchurch to Auckland. If 176 of the people that boarded the plane are male, how many are female? 

In pairs I asked my learners to read the question aloud then reread it and find the maths. Once they had the numbers to work with I asked them to decided were they being asked to find a sum or an addend. When that had been established I asked them to use what they already knew to decide which number operation would be the best choice to help them find the answer. Alongside each step we revisited the fact that we were inferring (ie: using the clues given with our prior knowledge to help us find the answer). 

What began as a scaffolding strategy evolved into a deep dive into a learning experience full of rich discussion for all my learners that I hope to build on to strengthen the connections between inference in reading and inference in maths.

Strengthening my connections to Inference...

Maths questions include numerical information that when combined with a mathematical symbol (or the text version of this), prompts students to use what they already know to help them make inferences about what they need to do with the information to find the answer. Having had a rich discussion about this with my friend and colleague Sheree Hodge (Ranui Schoo In-school Maths CoL teacher), I decided to dig a little deeper to strengthen my own understanding.

Inference helps students comprehend text. It is the skill of using what you already know to work out what you don't know based on the clues given to help you visualise what is happening. Simply put, inferencing involves using what you know to make a guess about what you don't know. There are two types of inference, default inference (automatic assumptions) and reasoned inference (a conclusion made based on the information available). 'Once students have identified the premises on which they've based their inferences, they can engage in the most powerful part of the process—examining the validity of their thinking.' Marzano (2010).

'Inferences are made when information the author assumes can be logically made are left out,' Carr (1983). We make inferences every day, and often because this is automatic don't realise what we have inferred wasn't included in the information we were given. If we are driving and suddenly the flow of the traffic slows down we infer that there is a problem ahead by exploring possibilities (maybe the traffic lights are short phasing, or someone has broken down or maybe there has been an accident) to make sense of the situation. No one gave us these details but as the traffic flow has slowed we know there is a problem and automatically draw on what we know to be possible reasons to help us explain the situation. In reading we 'read between the lines' to use the information given about a character or situation to visualise what is happening then use what we know to be possible behaviours or outcomes to help us draw conclusions about what might happen next or explain why something happened the way it did. In maths this is no different because written maths is inference. Students have to infer from the language in the written problem what numbers are involved, the number knowledge they require and whether or not they're trying to find a sum or a missing addend. 

From a word problem our learners need to be able to work out what the mathematical problem is first and in order to do this they need to understand the literacy of maths. If you think about this in relation to English, think about how as a teacher you use word studies to grow vocabulary knowledge. We help our learners explore the different synonyms for a word by unpacking the definition and talking about the different ways that word can be used in a sentence. We then scribe the student generated examples to allow our learners to make a visual connection to what this looks like in context. There is no difference in maths. If addition is used as the example, we need to talk about what addition looks like eg: A + B = C or B + A = C and explore the synonyms of 'add' to grow vocabulary knowledge in context. Once we have this knowledge we then need to use it help us make the inferences needed to find the sum (eg: A + B = ____), or the missing addend (eg: A + ___ = C). What I mean by that is once the students have identified the key mathematical words and the numbers they need to work with, they must then use this knowledge to infer what it is they are being asked to do with the information they have.

My next step is to find out if my learners know and understand what inferring means in a reading context, then see if they are able to transfer this knowledge to a maths context.

Readings to support my learning:

• Marzano, R. (2010). Teaching inference. Educational Leadership, 67(7), 80-01
• Carr, K (1983). The Importance of Inference Skills in the Primary Grades, p 518-522
• Making Inferences to Improve Reading Comprehension
• Reading Rockets
• Why you need to teach inference to struggling readers

Collegial Observations

This morning +Karen Ferguson from Tamaki College visited Learning Space 2 to observe a few of the ways we build connections to literacy in our Maths lessons. Karen has written a detailed account of the teaching and learning she observed on her blogpost here.  

 

Karen taking part in our timed challenge

                

                     Purposeful group challenge to help strengthen connections to the vocabulary