# 5 ways grown ups can transform MATHS for their children

Given the performance and test-driven culture of our schools, with over-packed curriculum and stressed out learners, what can grown ups do to transform maths for their children?

*Su, 2020*

**"because every single one of us is, whether we realise it or not, a teacher of maths."**

**Here are some TRANSFORMATIVE steps you can take:**

While traditional narrow questions communicate to learners that mathematics is about recalling and applying a procedure, **OPEN TASKS** provide opportunities for learners to engage in what Stein et al. (1996) call “DOING MATHEMATICS” that is:

**“framing and solving problems, looking for patterns, making conjectures, examining constraints, making inferences from data, abstracting, inventing, explaining, justifying, challenging, and so on” ****(p. 456).**

Rich mathematical tasks also support the development of autonomous learners, as children are not dependent upon reproducing examples to gain the correct solution, rather they are encouraged to follow their own creative thinking and ideas (Silver and Stein, 1996; Silver, 1997). Several studies have shown the connection between the use of open tasks and the development or strengthening of learners growth mindsets (Boaler, 1998; Stohlmann et al., 2018; Sun, 2018).

Our** TASKS ***Build SENSE MAKING. Skipping the sense making step makes for fragile understanding and *cognitively expensive memorisation

*. When someone only memorises,*

**every new fact is like an island unto itself, and is more readily forgotten**

**.**In contrast, understanding patterns in math facts compresses the cognitive load required to recall related facts. Sense making promotes**DEEP**,**ROBSUST**and**FLEXIBLE**understanding, allowing learners to apply what they know to new problems.

It is part of our maths culture that being good at maths is synonymous with being quick with number problems and retrieving number facts from memory. As soon as children enter formal education they begin to associate being quick at maths with praise from teachers. **Yet, when teachers are asked why maths learning and is so time-based, they often struggle to give a response.** Often they will resort to emphasising that formal assessments require them to teach in ways that encourage children to get faster and faster at retrieving numerical facts, particularly multiplication facts.

Sadly, there is plenty of empirical and anecdotal evidence that tells us just how stressful and anxiety-provoking quick-maths can be.

*The myth that fast recall of basic math facts is good for learning has deep and pernicious roots. It comes from the best of intentions – who wouldn’t want kids to be good at calculating? But research shows that fact fluency – the ability to easily recall facts, like 3 x 5 = 15 is best developed from first making sense of arithmetic operations. In other words, the first step in building a mathematical memory is understanding how that maths works.*

Chinn (2009), found that the item, ‘having to work out answers to maths questions quickly’ was ranked as fifth out of 20 anxiety-provoking classroom experiences. **Why would a known stressor be thought of as the most appropriate learning strategy? This important question is one that has not been suitably addressed.**

Time may provide a way of grading children’s performance, which is then displayed on leader-boards, but consequences are

**a) The majority of children in a class cannot be the fastest**

**b) Some children will be slowest **

**c) Irrespective of their position within the hierarchy, children will unduly focus on the speed of their response as being the key factor, reinforcing the belief that “being good at maths means being quick at maths” rather than an emphasis on understanding the subject.**

The availability of technology and the internet has provided schools with the means to implement timed testing of facts but we should be asking **what purpose does it serve to be a few seconds faster at performing a times table test, or faster than one’s classmates? **

In my opinion this only provides more instances of perceived negative experiences, often associated with the development of maths anxiety and withdrawal.

Of course, some children enjoy the competitive nature of maths assessments, but these are often children who perform well anyway. For the majority, timed testing only ups the ante for fear of negative evaluation. **So, there are two ways to fail: being wrong and being slow.** Compared to other tasks, children (and many adults) find mental arithmetic challenging. It is irrational to emphasise quick responding. For example, being told to swim faster will not be efficacious if one has not mastered the basic techniques. Indeed, it is likely to lead to panic, and a general avoidance of swimming in the future.

Forcing a person to respond quickly represses metacognitive processes. Metacognition, or “thinking about thinking” (Flavell, 1979), refers to an individual’s mathematical reasoning and problem solving procedures. As outlined by Morsanyi et al (2019), maths anxiety may impact on such processes, suppressing strategy choice or appraisal of solutions. Learners need time to consider options, to decide which strategy and which solution they have more confidence in. This relates to a consistent finding within the academic literature, which is that maths anxiety is frequently correlated with response time, especially on problems that place greater demands on working memory, such as multi-step problems.

Doing maths quickly pressurises learners to rush into questions without overviewing and thinking. It discourages appraisals of answers and pre-and post-estimations. It does not encourage metacognition.

*Avoid a focus on speeded responses**Don’t over-emphasise quick responses**Avoid unnecessary competition and public displays of performance**Allow extra time if needed - if a child takes a particularly long time to perform a maths task, find out why. Don’t let this become an issue for the child.**Avoid inappropriate and pervasive messages that over-emphasise the importance of quick completion of every task in mathematics.*

It is not important to work quickly, and we now know that forcing kids to work quickly on maths is the best way to start maths anxiety for children, especially girls. Don’t use bland, meaningless fashcards or other speed drills. **Instead use visual activities such as...**

*These will promote SENSE MAKING and promote DEEP, ROBUST and FLEXIBLE understanding, allowing learners to apply what they know to new problems.*

Instead find the logic in learners thinking – there is always some logic to what they say. For example if your child multiplies 3 by 4 and gets 7, say – Oh I see what you are thinking, you are using what you know about addition to add 3 and 4, when we multiply we have 4 groups of 3.

## Mistakes are part of the learning process.

Reframe mistakes as **EXPLORATIONS**. Not having a correct answer doesn’t mean all thinking is incorrect. Asking kids to explain their thinking also helps in understanding what they know now, and what they might learn next. Questions about how a kid got an answer can get them thinking about what does not quite work and is worthy of revision. When you ask these questions, it’s good to have a poker face; if you broadcast that an answer is wrong or right, it can reinforce the belief that only right answers count.

**Did you readout BLOG on MATHS TALK? There is some FREE DOWNLOADABLE** **CONTENT** that supports this.

Just as teachers serve as role models for learners, parents serve as long-term role models and their beliefs can influence their children as children develop their own identities, values, and efficacy (Yee and Eccles, 1988; Eccles et al., 1990; Tiedemann, 2000; Jacobs, 2005).

What’s interesting about maths is that it’s socially acceptable to say things like, ‘I hate math,’ But you wouldn’t hear people bragging about how they’re 'bad at reading.'

In an important study researchers found that when mothers told their daughters they were not good at math in school, their daughter’s achievement declined almost immediately (Eccles & Jacobs, 1986).

In a new study neuroscientists Erin Maloney and colleagues found that **parents’ math anxiety reduced their children’s learning of maths**, but only if parents helped their children on math homework (Maloney, Ramirez, Gunderson, Levine, & Beilock, 2015) If they did not help them on homework, the parents’ math anxiety did not detract from their children’s learning.

**In summary, the parents’ math knowledge did not turn out to have any impact, only their level of math anxiety**.

Parents' math anxiety may be subtly communicated to children throughtheir role of helping (or not helping) children with their math homework (Bhanot and Jovanovic, 2005; Maloney et al., 2015).

Be mindful of what you say about your own math fear around your children and try to avoid “**perpetuating any negative stereotypes about math, gender-based or otherwise.”** Many teachers and parents try to be comforting and sympathetic about maths, telling girls not to worry, that they can do well in other subjects. We now know such messages are extremely damaging.

# Jo Boaler reminds us that Parents’ Beliefs about Math Change Their Children’s Achievement'

If you recognise that you are a survivor of math trauma, take heart. You are not alone, and there are ways to heal. It starts with understanding that mathematics is broad and beautiful – most of us are much more mathematical than we think.

A wide range of evidence points to the need for learners to have a growth mindset as they approach their learning, but recent critiques of mindset have highlighted the need to **change teaching approaches**, to transfuse mindset ideas throughout teaching.

In recent years there has been considerable attention paid to the idea of mindset, a construct developed and researched by Carol Dweck. Dweck has shown that students with a “growth mindset”, who believe that they can learn anything and that their intelligence develops as they learn more, outperform those with a fixed mindset who believe their intelligence is fixed (Aronson et al., 2002; Good et al., 2003; Blackwell et al., 2007). Dweck’s book summarising mindset is an international best seller (Dweck, 2007) and her ideas have been used by tens of thousands of schools worldwide, as well as businesses, sports teams, and parents. Despite the extensive research base showing the impact of mindset changes, critiques of the concept have emerged. Dweck herself has now written about the dangers of “false growth mindset” work in schools, when teachers learn only to praise effort, but do not implement teaching strategies to help develop growth mindsets.

A key part of a mathematical mindset teaching approach (Boaler, 2016, 2022) advocates the use of **OPEN TASKS**, that are **“low floor and high ceiling****” **— these are tasks that all learners can access but that extend to high levels, and that can be approached in multiple ways. Mathematics classrooms are typically filled with closed, narrow questions – that can contravene growth mindset messages.

Learners often interpret mathematics as a fixed subject, as questions have one right answer with one valued method. If questions are, by contrast, open, with invitations to children to draw, discuss, and make connections with prior knowledge, then they are more likely to see mathematics as a growth subject that they can learn (Boaler, 2002, 2019). These types of tasks also allow learners to engage in authentic mathematical thinking and reasoning in ways that more traditional problem sets do not allow (Schoenfeld, 2016).

**I’d love to hear your thoughts on ways grown ups can transform MATHS for their children. Which ideas resonate with you? What do you disagree with? All views are welcome - post in the comments. **

**Thank you for all you do to support your children's number journey. Thank you for watching and listening.**

**Love, Janey x**