Early mathematical performance of deaf and hard of hearing toddlers in family-centred early intervention programmes

ABSTRACT

Research indicates that establishing a strong foundation in early mathematics is essential for later academic learning. Previous research with students who are deaf or hard of hearing (DHH) has shown varying differences in the performance and achievement when compared to typically hearing (TH) students. While the majority of research in this area has been conducted in the United States, studies in other countries suggest that these differences may be global. The present study investigated the early mathematics abilities of 3-year-old DHH children enrolled in family-centred early intervention in the Netherlands. Fifty-three DHH and TH children were given an adapted version of the Early Mathematics Performance Diagnostic. Results showed that on average, the DHH and the TH children performed similarly on all domains, except for Measurement. Likewise, both groups showed similar mathematical knowledge in most early mathematics tasks measuring sub-concepts such as counting objects, shape matching, or measuring weight. Differences were identified in some basic tasks measuring the sub-concepts (e.g. rote counting, measuring time, solving puzzles), however, not on the more advanced tasks measuring these same sub-concepts. These findings are important for parents, teachers, and early interventionists.

KEYWORDS:

• Deaf
• hard-of-hearing
• mathematics
• early intervention

Research indicates that establishing a strong foundation in early mathematics is essential for later academic learning (Bailey et al., 2014; Claessens & Engel, 2013; Denton & West, 2002; Duncan et al., 2007; Jordan et al., 2009; Sarama et al., 2012). This is not only the case for mathematics but also for other content areas such as literacy (Claessens & Engel, 2013; Duncan et al., 2007) and later language proficiency (Sarama et al., 2012). In fact, early mathematics skills have been found to be a stronger predictor of later academic achievement than any other early assessment (Duncan et al., 2007). In their meta-analysis on six longitudinal datasets, totalling approximately 35,000 children from the United States, Great Britain, and Canada, Duncan et al. (2007) found that the predictive power of early mathematics skills (number knowledge, counting, addition, number sequence, ordinality, and relative size) at the ages of five and six years for later school success (both mathematics and reading) was stronger than that of early reading skills. Further, the predictive power of early mathematics skills for later school success lasted longer than that of early reading skills. Given the importance of STEM across the globe to solve world problems and advance societies, it is imperative that we understand the variations in children’s understanding of these concepts from an early age.

Previous research with students who are deaf or hard of hearing (DHH) has shown varying differences in mathematics performance and achievement (Allen, 1995; Ansell & Pagliaro, 2006; Foisack et al., 2013; Henner et al., 2021; Mitchell, 2008; Nunes & Moreno, 2002; Traxler, 2000; van der Straaten et al., 2021). While many of these studies have pointed to a “delay” in achievement, as compared to their typically hearing peers, they do not consider the whole child; that is, the fact that many of the DHH children in their samples may not have had equal proficiency in language and/or arguably the same access and/or experiences. The few studies that have taken factors such as these into consideration (Ansell & Pagliaro, 2006; Henner et al., 2021; Hrastinski & Wilbur, 2016) showed that DHH students display differences (not necessarily “delays”) in performance and/or the same achievement in mathematics as their typically hearing peers.

Few studies over the years have investigated the mathematics performance of very young DHH children before they enter school (Kritzer, 2009; Leybaert & Van Cutsem, 2002; Pagliaro & Kritzer, 2013; Zarfaty et al., 2004), most of which focused on the area of number only. Again in most of these studies, results presented DHH children between the ages of 2;6 and 6 years as behind in number knowledge (i.e. rote counting, object counting, number comparisons, number facts). Exceptions include Zarfaty et al. (2004) which showed that young DHH children’s number representation was not different from typically hearing children. In this study, the DHH children were as able as the typically hearing children in reconstructing a set of bricks from a visual example. In addition to number, Pagliaro and Kritzer (2013) included in their study the areas of geometry, measurement, problem-solving and operations, patterns, reasoning, and algebra. Using both formal and informal measures, the researchers examined the performance of DHH children, ages 3–6 years, against a developmental trajectory of early mathematics concepts and skills. Results showed areas of strength (e.g. shape and geometry) and areas in need of attention (e.g. measurement of time and sequence). Thus, the few studies conducted on very young children (pre-school) support that differences between DHH and typically hearing children may begin even before formal schooling (Kritzer, 2009; Pagliaro & Kritzer, 2013).

While the majority of research in this area has been conducted in the United States, there is reason to believe that these differences may be global. Foisack et al. (2013) investigated the mathematics achievement of DHH students (ages 16-18) in Sweden and found significant differences between them and typically hearing children on the national subject test. Studies across mathematics topics from the UK, Brazil, Norway, and Italy, outlined in Gottardis et al. (2011) also report differences, some in favour of DHH children. A 10-year longitudinal study including more than 3.3 million children from age 5 years, of which approximately 9000 wore assistive listening devices, was conducted in the Netherlands with data obtained from the government (i.e. Statistics Netherlands). Findings showed that DHH children in integrated educational settings attained lower levels of achievement at the end of primary school in the areas of language and mathematics than did their hearing peers (van der Straaten et al., 2021); however, those differences were erased by the end of secondary school. Those DHH children who did not attend school in an integrated setting however, remained behind both the typically hearing students and those DHH students who were integrated. Again, in these studies, no outside factors were considered. Importantly, no study has documented the mathematics understanding of young DHH children in the Netherlands. Given that such differences exist based on the van der Straaten, et al. study, it is critical to focus on mathematical development in DHH children in the Netherlands before they start school.

Early intervention of DHH children in The Netherlands

In the Netherlands, Family-Centred Early Intervention (FCEI) is provided to DHH children between the ages of birth to approximately 4 years (the age at which most children in the Netherlands start formal schooling) and their families. The main aim of FCEI is to support parents in promoting their child’s development. During frequent home sessions, early interventionists guide and support parents in fostering their child’s development in all areas – cognitive, linguistic, and academic. In addition, parents can attend various courses (e.g. sign language courses, communication courses, and interactive reading courses) at the FCEI centre together with other parents, networking families who share experiences. It is critical that DHH adults be involved in early intervention programmes as educational, cultural, and linguistic specialists and models (Gale et al., 2021; Moeller et al., 2013). Thus, knowledge about the strengths and challenges of young DHH children in their early mathematics performance can inform FCEI programmes in helping parents of young DHH children to promote early mathematics skills at home.

Studies with typically hearing children have found a strong relation between the home environment and children’s mathematics development. For example, children who engage in more mathematics activities in the home have been found to have higher mathematics abilities (Kleemans et al., 2012; Skwarchuk et al., 2014; Thompson et al., 2017). Also, children whose parents incorporate more “mathematics talk” in their interactions with them show better mathematics performance (Gunderson & Levine, 2011; Ramani et al., 2015; Susperreguy & Davis-Kean, 2016). Likewise Pagliaro and Kritzer (2010) and Kritzer and Pagliaro (2013a, 2013c) showed the effect of parent mediation and discussion related to mathematics surrounding everyday events. In Pagliaro and Kritzer (2010), the authors analysed the differences in parent–child interactions between those children with relatively high and low mathematics knowledge. The children with relatively high mathematics knowledge had parents who provided rich interactions that included references to time and that focused their attention to detail, comparisons, and problem solving (in the general sense). The researchers incorporated this information in the latter studies (Kritzer & Pagliaro, 2013a, 2013c) where they coached parents to interact and specifically incorporate and mediate their DHH children’s mathematics learning within everyday tasks. In each of these studies, the use of mathematics vocabulary increased in both parents and children, parents behaviour positively changed and in the case of the latter investigation, the children increased in their mathematics knowledge.

The original intent of the present study was to replicate the Kritzer and Pagliaro (2013a, 2013c) study in the Netherlands. Unfortunately however, the COVID-19 pandemic halted the investigation before the work with parents could begin. The current analysis does provide, however, a focused replication and extension of Pagliaro and Kritzer (2013); that is, an investigation into the understanding of early mathematics by 3-year-old DHH children and their TH peers in the Netherlands. The present study highlights both the strengths and challenges of these children’s mathematics understanding. It is the first of its kind to focus on 3-year-old DHH children in the Netherlands, and includes various domains and concept areas within early mathematics. The central research question is: What are the strengths and challenges of deaf/hard-of-hearing (DHH) 3-year-olds in early mathematical knowledge and skills? The next section will present the methodology used to answer this research question including participants, instrument, and procedure.

Method

Participants

A total of 53 deaf and hard of hearing (DHH) and typically hearing (TH) children, aged between 36 and 50 months (M = 41.2 months), participated in this study, consisting of 22 DHH children and 31 TH children. Characteristics of the samples are reported in Table 1. All DHH children were enrolled in FCEI, and were recruited to participate through three FCEI centres. The TH children were recruited through well-baby clinics and regular day-care centres. The TH children were included in the study if they had passed the neonatal hearing screening. In both groups, the native language of one mother was a spoken language other than Dutch. No statistically significant differences were found between the two groups with the exception of mother’s education where the TH group had a higher level of mother’s education than did the DHH group. All parents gave written informed consent for their and their child’s participation in the research.

Table 1. Characteristics of participants.

Characteristic	DHH	TH
No. of children	22	31
Age, mean (SD) months	41.4 (3.8)	40.9 (3.2)
Age, range months	36–50	36–50
Gender, no (%)
Male	11 (50%)	18 (58%)
Female	11 (50%)	13 (41%)
Maternal educational level, mean (SD)^a	2.55 (0.5)	2.84 (0.4)
Level of hearing loss
Hard of Hearing, no (%)	9 (49)	NA
Deaf, no (%)	13 (51)	NA
Type of hearing device
Hearing aid, no (%)	12 (55%)	NA
Cochlear implant(s), no (%)	9 (41%)	NA
None	1 (4%)	NA
Parental hearing status
Hearing	17 (77.3)	30 (96.8)
One DHH parent	4 (18.2)	1 (3.2)
Two DHH parents	1 (4.5)
Unknown	2 (9.1)
Communication mode used with the child^b
Sign language only	2 (9.1%)
Spoken language only	3 (13.6%)	31 (100%)
Combination of spoken language with signs and/or sign language	14 (63.6%)
Unknown	3 (13.6%)

^a Maternal educational level was divided in three levels: low (1) =primary education, intermediate preparatory vocational education or level 1 of secondary vocational education; medium (2) = secondary vocational education, senior general secondary education or pre-university education; and high (3) = higher vocational education or academic education.

^b As reported by the parent.

Instrument

The Early Mathematics Performance Diagnostic (EMPD; Kritzer & Pagliaro, 2013b) was used to test the children’s mathematics understanding. The EMPD is a mathematics assessment designed to address the five domains of mathematics competence (i.e. number, geometry/spatial sense; measurement; problem solving, and patterns, reasoning and early algebra) using performance-based tasks that are engaging, motivating and meaningful for young (ages 3–5 years) children. There are forty-six tasks contained within the EMPD that target various sub-concepts under each domain. The tasks address 1–3 developmental levels as appropriate per sub-concept. These levels are labelled as “blue” (roughly corresponding to what is typical at age 3 years), “green” (roughly corresponding to what is typical at age 4 years), and “orange” (roughly corresponding to what is typical at age 5 years). The tasks are colour-coded rather than age-coded to put the focus on a developmental track rather than mastery of an age-dependent skill. The tasks are performance-based and designed to appeal to the interests and activity levels of preschool-aged children. They involve hands-on manipulation of familiar, motivating, and engaging materials (e.g. cookies, brightly coloured blocks, and stuffed animals) as well as full body movement (e.g. jumping and moving about the room).

The EMPD was translated into Dutch for administration with Dutch 3-year-olds in the present study, and some pictures were changed to reflect Dutch culture, however tasks were unaltered. Given the age of the participants in the present study, only the tasks at the blue and green levels were translated. All blue level tasks were given to the children. If the child was independently successful with the blue level task and if there was a green level task to follow in the EMPD, then the child was given an advanced task, the green level task, as well. The abbreviated Dutch version of the EMPD contained a total of 27 tasks, 16 at the blue level and 11 at the green level. The sub-concepts (i.e. knowledge and skills) included at these levels under the number domain are rote counting; counting objects; subitising; more/less; and one-to-one correspondence. Sub-concepts under the geometry domain and spatial sense are part/whole relations; shape matching (identical, varying in size, varying in orientation), identification, and sorting. For the domain of measurement, sub-concepts address time; size; and weight. For the domain problem solving/operations, the only sub-concept at this level is story problems. Finally, within the domain of patterns, reasoning, and algebra, sub-concepts include matching, repeating and growing patterns, and sequencing.

Per the EMPD directions, each child was given three opportunities to accomplish a task: unassisted, guided, and modelled (some tasks did not allow for guidance and/or modelling). The first opportunity, “unassisted,” presented the child with the stimulus only, no intervention by the administrator. If the child struggled with this, the administrator would provide the child with “guidance” to the stimulus per the EMPD directions. For example, in rote counting “guidance” is directed as prompting the child to continue counting by asking “what’s next?” several times until the child can proceed on their own. If the child continued to struggle, the task was “modelled” for the child by the administrator, again per EMPD directions. After the task is modelled, the child is expected to continue the task on his/her own. For example, in rote counting “modelling” constitutes the administrator counting “one, two, three” and then asking the child to try on their own. If the child was correct unassisted on a task, the developmentally advanced green level task was given if available. If a green level task was not available, the child was given the next blue level task until all the tasks were given.

In order to calculate a total score on the domains, performance on each task was scored per EMPD directions as 3 for accomplished unassisted, 2 for accomplished with guidance, 1 for accomplished with modelling, and 0 (incorrect) if the child could not answer correctly regardless of the degree of assistance. The task was scored as missing if it was not possible to administer due to distraction, which sometimes happens with 3-year-old children.

Procedure

The present analysis is part of a larger study in the Netherlands examining exposure to early numeracy concepts in the home environment. Administration of the EMPD took place during a home visit by one of the five members of the Dutch research team (two of which are authors here). The members were either a researcher or a professional working in the field of family-centred early intervention. The EMPD contains clear instructions for the administrator on what to say when providing guided or modelled assistance and all of the test administrators received training in the administration of the EMPD. Each administrator also did a practice run with a hearing child who was not a participant in the present study.

All children were administered the EMPD in their preferred language/mode of communication. Prior to the home visit, the early intervention provider was consulted on the DHH child’s preferred communication. The EMPD was administered in either spoken Dutch only, spoken Dutch supported by signs, or Dutch Sign Language for the DHH children, and in spoken Dutch for the TH children. Four of the administrators are experienced users of Dutch Sign Language and did the testing with the children who used some form of signing in their communication. At the end of the EMPD administration, the children received a picture book as a thank you for their participation.

In addition, parents completed a questionnaire on various background characteristics including maternal educational level, parental hearing status, communication mode with the child, and mother language background during a home visit.

The study was conducted in accordance with the Netherlands Code of Conduct for Research Integrity (2018). This Code was adopted by the Royal Netherlands Academy of Arts and Sciences (KNAW), the Netherlands Federation of University Medical Centres (NFU), the Netherlands Organisation for Scientific Research (NWO), Associated Applied Research Institutes (TO₂ federation), the Netherlands Association of Universities of Applied Sciences and the Association of Universities in the Netherlands (VSNU).

Data coding and analyses

The data collected via the background questionnaire were coded and entered into SPSS in order to describe the participant groups (see Table 1). Data collected via the EMPD were also entered into SPSS. Raw scores for each task were entered as 3, 2, 1, or 0 accordingly (see above). Blue and green level scores per domain were aggregated, resulting in a possible total score of 30 for number, 24 for geometry, 15 for measurement, 3 for story problems, and 15 for patterns, reasoning, and algebra. Then, for the blue and green levels separately, scores were transformed into a categorical variable indicating whether the child was able to accomplish the task without any assistance (score 1) or needed assistance (guidance or modelling; score 0) or was unable to do the task (score 0).

The raw scores were used for a descriptive analysis of the children’s performance. An independent-samples t-test with the domain scores was used to compare the performance of the DHH and TH children on the separate mathematics domains. A further comparison on the sub-concepts was made using Chi Square tests on the categorical data indicating whether a child had accomplished a task without any assistance or not.

Results

Tables 2 and 3 provide a descriptive overview of the performance of the DHH and TH children on the EMPD tasks, accomplished unassisted or with guidance or modelling. These data show that in both groups, at least some children, and for many sub-concepts the majority of children, were able to accomplish the tasks unassisted. Likewise for most sub-concepts, there were children who could not accomplish the tasks regardless of the amount of assistance. For the DHH group, there were 4 sub-concept tasks (all within the Geometry domain) in which all of the children were successful on their own or with some form of assistance (i.e. puzzles, matching identical shapes, matching shapes of different orientations, and sorting). For the TH group, there were 2 such sub-concept tasks (i.e. puzzles in the Geometry domain and measurement of weight in the Measurement domain) in which all of the children were successful on their own or with some form of assistance.

Table 2. Number of DHH children by performance on the EMPD tasks at the blue level.

Items	n	Incorrect	Modelled assistance	Guided assistance	No assistance
Number
Counting Rote	20	5	1	1	13
Counting Objects	21	6	–	3	12
Subitize	21	11	–	–	10
More/Less	22	13	2	–	7
One to One	22	7	7	–	8
Geometry
Puzzles	22	–	2	6	14
Shape Naming	22	13	–	–	9
Shape Matching identical	21	–	–	–	21
Shape Matching – vary in size	21	1	–	–	20
Shape Matching – vary in orientation	21	–	–	2	19
Sorting	19	–	1	1	17
Measurement
Time	22	9	2	4	7
Size	22	6	4	6	6
Weight	22	1	–	1	20
Problem Solving
Story problems	22	12	2	1	7
Patterns, reasoning, and algebra
Sequencing	21	6	2	2	11
Matching	20	1	2	1	16
Simple Repeating	15	11	–	2	2

Table 3. Number of TH children by performance on the EMPD tasks at the blue level.

Items	n	Incorrect	Modelled assistance	Guided assistance	No assistance
Number
Counting Rote	29	2	1	-	26
Counting Objects	31	5	–	2	24
Subitize	31	21	–	–	10
More/Less	30	5	–	3	22
One to One	31	8	6	–	17
Geometry
Puzzles	31	–	–	2	28
Shape Naming	31	22	–	–	9
Shape Matching identical	31	1	–	–	30
Shape Matching – vary in size	31	2	–	–	29
Shape Matching – vary in orientation	31	1	–	–	30
Sorting	30	2	1	–	27
Measurement
Time	31	8	–	3	20
Size	30	3	10	3	14
Weight	31	–	–	–	31
Problem Solving
Story problems	29	11	–	3	15
Patterns, reasoning, and algebra
Sequencing	30	11	–	1	18
Matching	31	1	2	2	26
Simple Repeating	30	18	1	4	7

For the DHH group, the task of simple repeating patterns seemed to be the most challenging as defined by the number of children who were not successful versus those who were (11 vs 4 respectively). This task was also challenging for the TH group but not by as much (18 unsuccessful vs. 12 successful). Tasks associated with the sub-concepts of more/less (number), naming shapes (geometry) and story problems (problem solving) were also challenging for the DHH group. For the TH group, additional challenges were found in the sub-concepts of subitising (number) and naming shapes (geometry).

To analyse the mathematics performance of the two groups (DHH and TH), the total scores per domain were compared. Table 4 shows the mean scores per domain. T-test analyses showed no differences between the two groups on the domains of number, geometry, problem solving, and patterns, reasoning, and algebra. However, in measurement the DHH group performed significantly lower than the hearing group (t(50) = −2.27, p = .028).

Table 4. Mean scores per domain by group.

	n DHH/TH	DHH M (sd)	TH M (sd)
Number	20/28	11.95 (8.95)	14.46 (6.47)
Geometry	19/30	19.11 (2.92)	19.07 (3.01)
Measurement*	22/30	7.68 (3.15)	9.37 (2.21)
Problem Solving	22/29	1.14 (1.39)	1.76 (1.43)
Patterns, reasoning, and algebra	14/29	7.17 (3.01)	7.00 (3.20)

*Statistical significance at .05 level.

Additional analyses were conducted to look into performance on the individual tasks within the concept domains. Table 5 shows the percentage of children in each group (DHH and TH) who accomplished the tasks at the blue level without any assistance. Results of the Chi square tests indicated a significant difference between the two groups on the tasks for rote counting (X²(1) = 4.43, p = .035), more or less (X²(1) = 8.89, p = .003), time (X²(1) = 5.51, p = .019), and puzzles (X²(1) = 5.57, p = .018). The percentage of TH children who solved these tasks without any assistance was greater than the percentage of DHH children.

Table 5. Percentage of DHH and TH children who accomplished the tasks at the blue level without any assistance.

	n DHH/TH	DHH (%)	TH (%)
Number
Counting Rote*	20/29	65.0	89.7
Counting Objects	21/31	57.1	77.4
Subitize	21/31	47.6	32.3
More/Less**	22/30	31.8	73.3
One to One	22/31	36.4	54.8
Geometry
Puzzles*	22/31	63.6	90.3
Shape Naming	22/31	40.9	29.0
Shape Matching identical	21/31	100.0	96.8
Shape Matching – vary in size	21/31	95.2	93.5
Shape Matching – vary in orientation	21/31	90.5	96.8
Sorting	19/30	89.5	90.0
Measurement
Time*	22/31	31.8	64.5
Size	22/30	27.3	46.7
Weight	22/31	90.9	100
Problem Solving
Story Problems	22/29	31.8	51.7
Patterns, reasoning, and algebra
Sequencing	21/30	52.4	60.0
Matching	20/31	80.0	83.9
Simple Repeating	15/30	13.3	23.3

*Statistical significance at .05 level.

**Statistical significance at .01 level.

Advanced task performance

Children in both groups who accomplished the sub-concepts at the blue level without any assistance were also administered the tasks for that sub-concept at the green level, a developmentally advanced level, if available (see Tables 2 and 3 for the number of children in each group who accomplished the blue level without any assistance and thus took the green level tasks). The sub-concepts measured at the green level were rote counting, counting objects, subitising, more/less, and one-to-one correspondence for the domain of number. Sub-concepts part/whole relations and sorting were measured for the domain of geometry, sub-concepts time and weight for measurement, and sub-concepts sequencing and repeating patterns for the domain of patterns, reasoning, and algebra. No sub-concepts for problem solving were measured at the green level.

Table 6 shows the percentage of children from the total groups of DHH and TH children who were able to accomplish the green level tasks without any assistance. For example, of the 20 DHH children who were given the blue task in rote counting, 47.6% were also able to accomplish this task at the green level without any assistance. Chi square tests indicated that the DHH and TH children did not perform differently on the green tasks, except for the task measuring the sub-concept more or less under the number domain. Here, the percentage of TH children who accomplished the green task without any assistance was significantly higher than in the DHH group (X²(1) = 4.20, p = .040).

Table 6. Percentage of DHH and TH children who accomplished the tasks at the green level without any assistance.

	n DHH/TH	DHH (%)	TH (%)
Number
Counting Rote	20/29	47.6	51.7
Counting Objects	21/31	23.8	35.5
Subitize	21/31	19.0	9.7
More/Less*	22/30	9.1	33.3
One to One	22/31	31.8	32.3
Geometry
Puzzles	22/31	18.2	19.4
Sorting	19/30	73.7	83.3
Measurement
Time	22/31	4.5	0.0
Weight	22/31	50.0	74.2
Patterns, reasoning, and algebra
Sequencing	21/30	23.8	6.7
Simple Repeating	15/30	13.3	10.0

*Statistical significance at .05 level.

Discussion

This study investigated the early mathematics abilities of 3-year-old Deaf and Hard of Hearing (DHH) children enrolled in family-centred early intervention (FCEI) and 3-year-old typically hearing (TH) in the Netherlands. Using a performance-based assessment designed for young children to address sub-concepts within five domains of early mathematics competence [i.e. the Early Mathematics Performance Diagnostic (EMPD; Kritzer & Pagliaro, 2013b); number, geometry/spatial sense; measurement; problem solving, and patterns, reasoning and algebra], we identified both strengths and challenges displayed by each group.

Overall, both groups performed equally within each domain on the blue tasks (roughly equivalent to 3 years of age), except for the measurement domain where the TH group outperformed the DHH group. For both groups, the strongest domain was geometry and the most challenging was problem solving. These results are in line with those of Pagliaro and Kritzer (2013) who also found strengths in the geometry domain and challenges in the area of measurement in DHH children in the United States. Of the twenty participants in the Pagliaro and Kritzer study, four were three years old, nine were four years old, and seven were five years old. It is interesting that findings in the Dutch sample of only three-year-olds mirror those of mostly older DHH children. It seems as if these strengths and challenges for the DHH group continue to follow the same path as children grow older. We encourage further, much-needed longitudinal investigations into DHH children’s mathematics performance to map development and inform pre-K education. The recent study by Cawthon et al. (2023) on growth trends in reading and mathematics beginning at grade 2 may be a good model to follow. We suggest studies beginning at a much younger age. Thus, it may be possible to identify the areas that need attention and avoid gaps in understanding and optimally build upon strengths.

To unpack the children’s understanding at a more detailed level, we analysed their performance on the sub-concepts within each domain. Although the percentages showed some variation in independent success, statistically these findings likewise showed that DHH children and TH children perform similarly at tasks roughly corresponding to the age of 3 years (as shown by unassisted success on blue tasks) and of 4 years (as shown on independent success on green tasks) across most sub-concepts. Exceptions were found in just four sub-concepts under the blue tasks including counting rote and more/less (number domain), puzzles (geometry domain), and time (measurement domain). For those children who attempted the green tasks, there was a significant difference in just one sub-concept, more/less (number domain). In all of these cases the TH children were more successful than the DHH group.

These findings are important for early intervention (EI) providers, in the FCEI programmes within the Netherlands, as well as globally. The focus of early intervention has historically been on language and social development and much less on mathematics. Incorporating more early mathematics into the EI curriculum either directly (i.e. with tasks and activities that include counting, puzzles, matching, etc.) or indirectly (i.e. “hidden” within social play or traditional language time), will not only support the development of mathematics but also target those areas in which DHH and typically hearing children may experience challenges. EI professionals may wish to look to established trajectory-based mathematics curricula/interventions such as Building Blocks (Clements & Sarama, 2007) for assistance.

In addition, providing parents with information, knowledge and skills to include “mathematical language” into their daily interactions with their young DHH children will support early mathematics development, and future academic achievement. “Math talk” used with young children has been shown to significantly relate to an increase in understanding of mathematical concepts (Klibanoff et al., 2006; Walkerdine, 1988). Previous studies on young DHH children showed that their parents use a limited variety of words during interactions compared to parents of typical hearing children (Ambrose et al., 2015; Dirks et al., 2020). It is therefore important to support parents in providing a rich language environment including “math talk.” Parents could be encouraged to play mathematical games with their DHH children, read books that contain mathematics (Pagliaro & Roudybush, 1998), such as counting games, and incorporate mathematics into daily activities with their children. To this effort, the Building Math Readiness in Young Deaf/Hard-of- Hearing Children: Parents as Partners (MRPP) Intervention by Kritzer and Pagliaro (2013a, 2013c) may be helpful. This programme helps parents of young DHH children strengthen their child’s readiness for school mathematics by teaching parents to include mathematics in natural interactions with their child. Parent training programmes in other areas, for example on shared reading, have shown to be effective in helping parents to adapt their behaviour (Dirks & Wauters, 2018). The MRPP programme has also been found to have a positive impact on both parents’ knowledge of early mathematics concepts and developmental sequence as well as parents’ ability to mediate these concepts to their young DHH children (Kritzer & Pagliaro, 2013a, 2013c).

Limitations

There are limitations with the present study that should be considered. First, the number of children in this study was relatively small which could impact the power of the analyses. For example, on the sub-concepts subitising and shape naming, a higher percentage of the DHH children succeed, but the difference with the TH group is not significant. Research with a larger sample may yield different results. Therefore, it would be wise to replicate this study with a larger group of children. Also, with a larger group, it would be possible to investigate what are the characteristics of the children who also succeed at the green level of the tasks without any assistance. Our sample was too small for these analyses.

Second, other data should be collected to examine the full context surrounding the children, for example on children’s language skills. Henner et al. (2021) showed that 8–18 year old children with better sign language (i.e. American Sign Language) skills also showed better mathematics skills. Similarly with TH children, language skills are strongly related to mathematical skills (Slot et al., 2021). The language factor may have played a role in the present study as well. For example, the blue tasks related to skills reflected in the measurement domain involved language. Children are successful if they can name the days of the week or can state that one bear is “big” and the other is “small.” Findings then may be a by-product of poor and/or limited access to language that the DHH children experience within their environments (and/or the resulting limited incidental learning). In fact, several studies have shown that DHH students who have a strong language base do perform at higher levels in mathematics, some on level with or above their typically hearing peers (Henner et al., 2021; Hrastinski & Wilbur, 2016; Kelly & Gaustad, 2006), reflecting as well the literature in general education that supports the link between the development of language and the development of mathematics (See Henner et al., 2021 for explanation). We did collect data on children’s language skills, but these were not complete and therefore could not be used in our analysis. In future studies, both sign language and spoken language skills should be measured and taken into account particularly in DHH children’s mathematical performance given what is known of their early access to a complete language.

Future research

The results of the present study show that both DHH and TH children in the Netherlands make a similar start in developing their mathematics skills. Both groups performed equally on most early mathematics tasks and children who grasp the early concepts seem to perform well on the more advanced tasks measuring these concepts as well. From our results, we suggest several designs for future studies. First, a design that collects longitudinal data is needed. The results from the present study show that on many tasks, a similar number of DHH and TH children independently succeeded, yet previous studies have shown that older DHH children may struggle with mathematics. Longitudinal analyses would determine if good mathematics skills at the young age of the DHH children, like those in the present study, hold as they become older and start formal schooling. Might the smaller number of significant differences on the green sub-concept tasks compared to the blue be an indication that strong earlier concepts build success? Further, understanding of DHH children early mathematics understanding using the EMPD and other measures should be undertaken across countries so as to establish a normative development of early mathematics concepts for DHH children and determine whether that trajectory is the same or different from TH children. If different, the subsequent curricular and instructional changes should be made. Finally, a study that includes one of the aforementioned trajectory-based interventions may help determine a different (not delayed) trajectory of development in early mathematics for DHH children, perhaps eradicating the “math gap” (Pagliaro & Kritzer, 2013) altogether.

Given the importance of mathematics understanding in all areas of academics and for professional success, these studies, and other related to mathematics education and DHH persons, are not only imperative, but also long overdue.

Acknowledgements

The opinions expressed are those of the authors and do not represent views of the Dutch Ministry of Health, the Institute of Education Sciences or the U.S. Department of Education.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Dutch Ministry of Health, Welfare and Sport (Ministerie van Volksgezondheid, Welzijn en Sport) and the Institute of Education Sciences, U.S. Department of Education [grant R324A090145 to Kent State University].

Notes on contributors

Loes Wauters

Loes Wauters is the program director of the Deaf and Hard of Hearing Research Program at the Kentalis Academy, Royal Kentalis, Utrecht, the Netherlands,. She is also professor at the Behavioral Science Institute, Radboud University, Nijmegen, the Netherlands.

Claudia M. Pagliaro

Claudia M. Pagliaro is a Professor in Deaf Education in the Department of Specialized Education Services, School of Education, University of North Carolina Greensboro, USA.

Karen L. Kritzer

Karen L. Kritzer is the director of the Deaf Education Program and an Associate Professor in the program of Lifespan Development and Educational Sciences, Kent State University, Kent Ohio, USA.

Evelien Dirks

Evelien Dirks is the director of the Deaf and Hard of Hearing Research and Development Program at the Dutch Foundation for the Deaf and Hard of Hearing Child, Amsterdam the Netherlands. She is a lecturer at the Developmental Psychology department of Utrecht University, Utrecht, the Netherlands.