Eight Pieces of the Learning Puzzle: How Teachers Can Help
Philippa Fabbri, director and founding member of Elsen Academy in Gqeberha (Port Elizabeth), in the Eastern Cape, discusses the learning puzzle: difficulties children may experience in relation to thinking with numbers and learning to read.
1. Thinking with numbers
Mathematics is a cumulative subject, and the learner must constantly integrate new and more sophisticated skills and concepts.
For students to progress to more complex tasks, a portion of mathematics knowledge must become automatised – in other words habitual. As basic abilities (such as producing addition and subtraction facts) become automatic, the learner can manage higher mathematical levels, such as the use of maths procedures (for example the steps for long division and the rules for multiplying fractions), the building of maths concepts (ratio and proportion), and the process of problem solving (as in maths word problems).
If a child does not have strong ‘sense’ of numbers, the teacher can try the following helpful tip. They can move the student through a sequence of understanding from concrete objects to semi-abstract representations, to abstract notions.
If, for example, a teacher is trying to help the student understand that 3 x 2 = 6, they might place three paper plates on the floor, put two blocks on each plate, and finally, count the number of blocks to arrive at the understanding that ‘three groups of two blocks equals six blocks’.
The semiabstract level of understanding involves the use of pictures or drawings to represent numbers, and the abstract level of understanding involves the use of numerals as representatives of the symbolic process, e.g., 3 x 2 = 6.
If a student does not understand that there are basic patterns in numbers, the teacher should encourage them to use a strategic approach for practising and recalling maths facts. An example is saying, ‘I don‘t know 7 x 6, but I do know that 7 x 5 = 35, so one more 7 makes 42’; or, ‘I know that 7 x 7 = 49, so one less 7 makes 42’.
Another helpful tip is to teach the commutative property of addition and multiplication to build awareness of number patterns. Regardless of the order in which the same numbers are combined, the sum is the same (e.g., 2 + 4 = 4 + 2) and the product also remains the same (e.g., 7 x 2 = 2 x 7).
Some students’ performance may be inconsistent. They may remember some maths facts while forgetting others. Let them use supplementary information for facts that are not already automatic. For example, maths fact tables and/ or grids may be kept on hand for reference during maths activities. As maths facts are mastered, remove the supportive prompts.
Some students may have difficulty remembering multiplication, division, and/or other facts while solving problems. Teachers can integrate, drill and practice activities into a fun format, such as a game with a deck of playing cards that students can play in pairs.
If a child experiences challenges when reasoning through a problem or using strategies effectively during problem solving, encourage them to explore multiple strategies that could be used for problem-solving. For example, ask students to find the length of the diagonal of a 12 cm x 16 cm rectangle. The intention is for students to recognise that the rectangle is made up of two right-angled triangles, and for them to apply the Pythagorean theorem. Two approaches to this challenge might be to either calculate by hand, or to use a calculator for the computation (12² + 16² = ?).
Mental pictures and mnemonics
A student may have difficulty using mental pictures (such as patterns or shapes) to represent maths concepts or may experience difficulty ‘seeing’ the maths problem in their mind. A helpful tip is to have students draw pictures to represent what is going on in a word problem. Students may draw actual objects from the problem, or they may represent objects with check marks or dots.
Providing a set of questions students can ask themselves to ‘jump start’ their problem solving, e.g., ‘What does this question remind me of?’, or ‘What am I being asked to do or find?’, or ‘What are the important facts or numbers?’ can be helpful for those who don’t know how to get started on word problems, or how to break problems down.
Mnemonics can also help students remember steps to maths algorithms. For example, the mnemonic ‘daddy, mama, sister, brother’ can be used for the long division algorithm (divide, multiply, subtract, bring down). Conquer further student confusion by teaching them to break multi-step problems into smaller parts.
For example, ask students to first look over the entire problem, then to break the problem into parts and identify which parts require the use of algorithm(s). Next, have them choose the algorithm to be applied for each part, and finally, ask them to solve the problem, reflecting on their answers at each step. Note: A checklist may come in handy for students to use to break down problems into stages.
Many students may have problems transferring concepts learned in the maths classroom to real life situations. Remind them to identify daily situations where they use maths skills, for example, when reading their school timetable or filling out order forms.
2. Mastering the challenges of reading
Students’ reading abilities depend upon many different factors. For some young people, sadly, reading can be frustrating. It is broadly divided into two academic skills: (1) word decoding, or accurate and rapid reading of words, and (2) comprehension, or understanding the intended message of a written passage. Both skills are facilitated by a combination of functions.
If any of your students has difficulty making rhymes or playing with sounds in words, read rhyming books aloud, or have the class listen to rhyming audio books. These experiences will reinforce the concept of rhyming and build students’ familiarity with rhyming patterns.
Let your students practise counting syllables by clapping or using their fingers to tap out the number of different sounds or phonemes in a word. This will help those who have difficulty putting syllables or sounds together to make a word. Students can also practise sorting words into categories using a variety of approaches (for example by rhyming, or by vocalising short versus long vowel sounds, first letter sounds, ending sounds, or middle sounds). This method will help those students who have difficulty segmenting or breaking down words into separate sounds.
When in doubt, sound it out
Children who do not know sound-symbol correspondences and cannot sound out individual words will benefit from the following teacher’s tip: explore the use of a systematic, explicit phonics instruction programme, one which moves the student through a series of developmental skills which lead to decoding abilities.
If any of your students seem to struggle with decoding words and have not established a bank of words that they can read easily or automatically, i.e., sight words, then you could try providing opportunities for them to develop reading fluency, which is the ability to read at a smooth and rapid pace. Encourage students to reread books they’ve read previously that are ‘easy’ for them; and have students read along with audiobooks or read along with you.
Another helpful tip is to allow students to read for comprehension during times when their mental energy is high, perhaps at the start of the day. Additionally, if they read with little self-monitoring of comprehension, and do not seem to know when they don’t comprehend a passage, then provide them with opportunities to practise using tools that promote and reinforce comprehension. For example, they can fill in outlines or speech bubbles and create semantic maps to organise and consolidate ideas as they read.
Many students lack the ability to pace themselves when reading. They may, for example, jump into difficult passages without previewing the content adequately, or read a passage too quickly to understand it. Teachers can help them control the tempo of their reading by using a metronome. Have them consider the amount of time they have to read a passage, and the amount of time they will need to fully comprehend what they read.
Lastly, consider providing struggling students with reading strategies. Encourage them to preview reading passages by talking about what they think a passage will be about before they read it, or have them preview questions that go along with the passage before reading.
In the next edition of Independent Education, we will discuss the difficulties children may experience in relation to written work and paying attention.