## Written by a group of visiting student teachers from the US

## What it’s like to be a teacher at the BSLRM Conference?

As a group of future primary and secondary math teachers in the U.S., currently at the University of Connecticut and visiting the University of Nottingham, we found this conference to be both useful and engaging. Of course there are many sessions from which to choose to tailor make your day so here are our reflections of just the a selection from the very few that we were able to attend and found most intriguing…..

### TIMES TABLES: Children learning *about* multiplication facts

We decided to start our day by attending a session that would apply to all of us. The researchers started by telling us that based on previous research, and their own past experiences as classroom teachers, they found that the majority of teaching and learning related to times tables that takes places in classrooms is still purely practice based. There is primarily a focus on strategies that involve memorization and recall. The researchers believe that this leads students to have a limited understanding of multiplication and also potentially has a harmful impact in the long-term because the focus is on testing not teaching multiplication.

The study allowed the researchers to explore their interest in children’s strategies for *working out *multiplication facts compared to children just *knowing* their times tables. The goal of the intervention involved in their study was for children to come to see times tables as a connected body of knowledge. The researchers were able to qualify what this looks like through teaching and observing 2 groups of primary school students who were previously thought of as struggling with math. The bulleted list below summarizes their findings.

**Student Strategies: Times Tables as a Connected Body of Knowledge**

- Awareness of the commutative law– I might not know my sevens for 7×5 but realise I know the answer to 5×7. I know my fives and I appreciate the answer will be the same.
- Use of nearby known facts– I know that 7×7=49 therefore 7×8 must be 56 as it will be an extra 7.
- The ability to scale answers up by doubling– Fours are double twos, eights double fours.
- The ability to scale answers down by halving– If I know 10 times something then I can calculate 5 times by halving.
- The ability to partition where appropriate– Particularly useful for multiplication involving numbers above 10. 13×9 = (10 x 9)+(3 x 9)
- Developing an awareness of the odd or even nature of an answer– This can help one spot an unexpected answer and allow one to check it.

After discussing these possible student strategies the presenters showed slides of student work from the study and encouraged comments and questions. The researchers also shared resources that they used with the student participants during the study which as teachers we certainly plan to use in our future classrooms. This was a really useful start to our day!

### Core Maths: Perceptions of its use and exchange value, and impact on student attitudes to mathematics.

There is nothing like Core Maths (CM) in the U.S. so we were very curious about it. The interviews of teachers shed light on the idea that CM gives students time to develop contextual applications of math, instead of rushing through the curriculum. The interviews also discussed the idea of the ‘use value’ CM has compared to its ‘exchange value’. Overall, the interview responses demonstrate that the ‘exchange value’ of CM is uncertain, but the ‘use value’ is widely acknowledged. Because of this, there is now some pressure in place on more universities to take the grades and UCAS points from CM. The researchers found that according to the students’ perceptions, CM is more student-centred than GCSE with the students thinking that they were given more opportunities within their learning while taking CM than in their previous math classes. One important aspect the researchers found in the students’ dispositions was that if the student made a positive decision to take the course, he or she had a more positive experience and rated math more highly. Overall, according to this research CM has proven to be valuable to students in many different ways and the researchers plan to move forward with the next cohort of CM students to see how the course is progressing and what more can be done.

The first phase of the research was about identifying children’s math knowledge in out of school activities and duties and the researchers introduced two children Ines and Edward. Edward is a fourth grader who helps his mother who works as a waitress; he regularly applies ideas of giving change and finding percentages. These topics are taught thoroughly at this point in school. This session was particularly interesting to attend as an American teacher because it is necessary for us to keep in mind the diverse backgrounds of the students we teach. We often do not think about a child’s life outside of the classroom- they are not just a student, but perhaps also a son/daughter, a brother/sister, a caretaker, a worker…. It is essential to adapt our math teaching to be applicable to students’ lives outside of the classroom, if we are to help them make connections and advance in their learning of math in school, and recognize the value and importance of math in everyday life. Giving tasks in which students are placed in scenarios like these on a daily basis can be very beneficial and crucial in the student’s attainment in the topic. Students are able to adapt their knowledge from their realities outside of the classroom to fit the material taught in the classroom.

**Conceptualizing the relationship between out-of-school experiences and math in school: a case of a working child in Mexico**

*Ines is an 11 year old garbage collector, and in this role, she regularly needs to apply concepts of proportional reasoning. These concepts can also be applied to tasks given in the classroom, to which Inés can greatly relate. Questions that might have some meaning to Ines might be of the form, “If Ines collected 10 kg of cardboard, and she was paid $1.50 per kilogram, how much money was Ines payed for that day’s garbage collecting?” Interestingly, more than 5 million children under the age of 16 work, in addition to going to school, in Mexico. This facilitates the possibility of incorporating the types of math that is applied in those jobs into the math explicitly taught in the classroom potentially allowing students to recognize how their math knowledge can transfer and be applied from one area to another and make connections across different aspects of day-to-day life.*

We thought it would be great to attend this session in order to take back some useful information and research to the U.S., since there is not a math course like this there. After attending this session we definitely gained quite a bit of insight as to why CM is so useful to students at this age. Since math is compulsory until what is equivalent to year 12 in the U.S., we think this could be a good alternative course for students to take during their High School career, especially if they are looking to take a math course that is directly related to the real world.

The second part of the session, which discussed the questionnaire data, focused more on students’ attitudes towards math with the students in the study being surveyed at the beginning and end of the course. The first questionnaire focused on how student-centered their learning had been thus far and the second questionnaire was about the students’ attitudes towards math. The first set of responses from the students were based on their GCSE learning and the second set was based on Core Maths, so the idea was to be able to compare the two to see the value in CM. The researchers first discussed some of the responses and overall findings they gained from the interviews they had conducted with 38 students and teachers from a variety of UK schools. These led the researchers to conclude that in the main students take CM either because their GCSE grades were below what they needed for progression quite generally or because it was needed for specific subjects, like engineering. After discussing these possible student strategies the presenters showed slides of student work from the study and encouraged comments and questions. The researchers also shared resources that they used with the student participants during the study which as teachers we certainly plan to use in our future classrooms. This was a really useful start to our day!

Overall, as math teachers, we had a really inspiring day which we found gave us a lot to think about in ways that related to all aspects of our classroom practice. We thoroughly recommend this day conference and only wish we were in the UK for longer so we can attend another!