Parental influences on the development of single and co-occurring difficulties in reading and arithmetic fluency

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ Pa en al in luences on he de elopmen o single and co-occu ing di icul ies in eading and a i hme ic luency © 2023 he Au ho s Published e sion Khanolainen, Da ia; Koponen, Tui e; Eklund, Kenne h; Ge ike, Geo gia; Psy idou, Ma ia; Le kkanen, Ma ja-K is iina; A o, Mikko; To ppa, Minna Khanolainen, D., Koponen, T., Eklund, K., Ge ike, G., Psy idou, M., Le kkanen, M.-K., A o, M., & To ppa, M. (2023). Pa en al in luences on he de elopmen o single and co-occu ing di icul ies in eading and a i hme ic luency. Lea ning and Indi idual Di e ences, 105, A icle 102321. h ps://doi.o g/10.1016/j.lindi .2023.102321 2023 Lea ning and Indi idual Di e ences 105 (2023) 102321 A ailable online 28 June 2023 1041-6080/© 2023 The Au ho s. Published by Else ie Inc. This is an open access a icle unde he CC BY license (h p://c ea i ecommons.o g/licenses/by/4.0/). Pa en al in luences on he de elopmen o single and co-occu ing di icul ies in eading and a i hme ic luency Da ia Khanolainen a , * , Tui e Koponen a , Kenne h Eklund b , Geo gia Ge ike b , c , d , Ma ia Psy idou b , Ma ja-K is iina Le kkanen a , Mikko A o e , Minna To ppa a a Depa men o Teache Educa ion, Uni e si y o Jy ¨ askyl¨ a, Finland b Depa men o Psychology, Uni e si y o Jy ¨ askyl¨ a, Finland c Cen e o In e disciplina y B ain Resea ch, Uni e si y o Jy ¨ askyl¨ a, Finland d Niilo M¨ aki Ins i u e, Finland e Depa men o Educa ion, Uni e si y o Jy ¨ askyl¨ a, Finland ARTICLE INFO Keywo ds: Reading di icul ies Ma hema ical di icul ies Home lea ning en i onmen Familial isk Como bidi y ABSTRACT This s udy in es iga ed how single and co-occu ing di icul ies in eading and a i hme ic luency de eloped among Finnish child en ac oss G ades 1–9 (N =2151). La en p o ile analysis among 391 child en who had eading and/o a i hme ic luency di icul ies in G ade 9 e ealed p o iles ha ollowed h ee dis inc pa e ns: eading di icul ies (N =121), ma hema ical di icul ies (N =94), and como bid di icul ies (N =176). The p o iles and ypical pe o me s we e compa ed on pa en al eading and ma hema ical di icul ies, pa en al ed- uca ion, he ea ly home lea ning en i onmen , and pa en al assis ance wi h school homewo k ac oss G ades 1–9. Resul s showed ha al hough pa en s whose child en had di icul ies p o ided hem wi h domain-speci ic sup- po ac oss all g ades, he amoun o suppo g adually declined and he pe o mance gap be ween he p o iles inc eased. 1. In oduc ion The end o comp ehensi e school is a c i ical ime poin — his is when adolescen s ace impo an choices ega ding hei u u e educa- ional pa hways. Un o una ely, hese choices can be nega i ely a ec ed by eading and ma hema ical di icul ies (RD and MD, espec i ely), as poo ounda ional academic skills a e a known isk ac o o la e lowe academic mo i a ion (Klauda & Gu h ie, 2015), highe le els o school bu nou and d opou a e compulso y educa ion (Ko honen e al., 2014), which can lead o unemploymen and men al heal h p oblems in adul hood (A o e al., 2019). In e na ional assessmen s show ha many eenage s s uggle wi h eading and ma hema ical asks ha a e well below hei g ade le el (Schleiche , 2018); ne e heless, longi udinal esea ch on eading and ma hema ical skill de elopmen mos ly ocuses on ea ly childhood and p ima y school educa ion, a ely ex ending in o educa ion du ing adolescence. Mo eo e , eading and ma hema ical skills a e in e ela ed (Ci ino e al., 2018) and di icul ies in hese do- mains o en co-occu (Moll e al., 2019), placing indi iduals a e en highe isk o he nega i e ou comes. Ne e heless, mos p e ious s udies examining he como bidi y o RD and MD a e c oss-sec ional and long- e m de elopmen al pa e ns leading o RD, MD, and como bid di icul ies emain o be iden i ied and examined. Du ing he las decade, an inc easing amoun o esea ch has examined he cogni i e ac o s ela ed o he co- a iance o eading and ma hema ical skills (Ci ino e al., 2018) and he como bidi y o di i- cul ies in hese domains (Lande l e al., 2009; Van Daal e al., 2012). Howe e , no ably less a en ion has been paid o he ela ed en i on- men al ac o s. Al hough nume ous s udies ha e shown posi i e co e- la ions be ween home lea ning ac i i ies and child en's eading (Dong e al., 2020) and ma hema ical skills (Duns e al., 2017), whe he he exis ing di e ences in he cha ac e is ics o he home lea ning en i- onmen could be ela ed o di e gen ou comes in adolescence is s ill unclea . S udying di e en ial pa hways o adolescen pe o mance and iden i ying he en i onmen al ac o s ha p edic hem can elucida e he isk and p o ec i e ac o s ope a ing in child en's e e yday li e. The main objec i e o his s udy is o gain new insigh s in o he de elopmen al pa e ns ha esul in RD and MD among adolescen s. To his end, we iden i y la en p o iles o eading and ma hema ical skill de elopmen among Finnish schoolchild en who demons a e low pe - o mance in eading and a i hme ic luency a he end o comp ehensi e * Co esponding au ho a : Uni e si y o Jy ¨ askyl¨ a, Huone RUU B325, Ruusupuis o, Al a Aallon ka u 9, 40600 Jy ¨ askyl¨ a, Finland. E-mail add ess: [email p o ec ed] (D. Khanolainen). Con en s lis s a ailable a ScienceDi ec Lea ning and Indi idual Di e ences jou nal homepage: www.else ie .com/loca e/lindi h ps://doi.o g/10.1016/j.lindi .2023.102321 Recei ed 29 July 2022; Recei ed in e ised o m 17 Ap il 2023; Accep ed 22 June 2023 Lea ning and Indi idual Di e ences 105 (2023) 102321 2 school (G ade 9, age 16). We hen compa e he skill le els o he low pe o ming p o iles o he skill le els o hei ypically pe o ming pee s o see how he pace o hei de elopmen di e s. In addi ion, we examine he ole o a ious amily ac o s in he de elopmen o oun- da ional academic skills. We include amily isk s a us (pa en al RD and MD), pa en al educa ion, and lea ning ac i i ies a home, as hese all a e linked wi h child en's eading and ma hema ical skill de elopmen (Dong e al., 2020; Duns e al., 2017; Esmaeeli e al., 2019; Van Be gen e al., 2014). To ou knowledge, his is he i s s udy wi h such an objec i e. This s udy builds on ou p e ious esea ch (Khanolainen e al., 2020) whe e we examined he e ec s o pa en al di icul ies and he ea ly home lea ning en i onmen on child en's eading and a i hme ic skills. In ha s udy we showed ha pa en al di icul ies had small p edic i e e ec s on child en's skills in he gene al popula ion sample. The o e all g oup le el analyses a e in o ma i e bu assume ha de elopmen al pa e ns and associa ions a e simila o all pa icipan s. This s udy is di e en as we ocus on he g oup o child en wi h lea ning di icul ies and es i he e a e di e en ial de elopmen al pa hs leading o lea ning di icul ies a he end o G ade 9. This app oach allows us o in es iga e he possibili y o he e ogeneous long- e m de elopmen al pa hways (including pa hways wi h single and como bid di icul ies). This is an impo an ex ension o he p e ious esea ch as we know ha eading and a i hme ic di icul ies a e o en como bid (Moll e al., 2019). Fu he mo e, in he p e ious s udy we speci ically examined he ole o he ea ly home en i onmen (measu ed when child en we e in kinde - ga en) in subsequen skill de elopmen . In his s udy, howe e , we inco po a e pa en al academic assis ance om G ades 1 o 9. 1.1. De elopmen al pa hways o eading and a i hme ic luency de elopmen Reading luency is mos o en de ined as he skill ha allows eading wi h speed and accu acy. I o ms he ounda ion o de eloping mo e complex skills, such as eading comp ehension (Flo i & Cain, 2011; Pikulski & Cha d, 2005). Simila ly, a i hme ic luency can be unde - s ood as he skill needed o speed and accu acy in simple ma hema ical calcula ions (addi ions, sub ac ions, mul iplica ions, and di isions). S ong a i hme ic luency is c i ical o u he ma hema ical de elop- men and di icul ies in a i hme ic luency a e an impo an p ecu so o di icul ies in highe -o de ma hema ical skills (Cowan e al., 2011; Jo dan e al., 2003). Th oughou his s udy we will e ain om using he e ms “dyslexia” and “dyscalculia”, ins ead op ing o “ eading di icul ies” and “a i hme ic di icul ies”. Ou pa icipan s comple ed only skill as- sessmen s ha a e su icien o iden i ying eading and a i hme ic di - icul ies bu a e no su icien o diagnosing ei he dyslexia o dyscalculia. Conduc ing ex ensi e diagnos ic assessmen s equi ed o a diagnosis was beyond ou s udy's objec i es. In addi ion, iden i ying eading and ma hema ical di icul ies ( a he han diagnosing dyslexia and dyscalculia) is in line wi h he suppo sys em p o ided wi hin Finnish educa ion whe e suppo is made a ailable based on eache s' iden i ica ion o lea ning di icul ies. No o icial diagnoses o dyslexia o dyscalculia a e needed o special needs suppo . A he same ime, i is likely ha a sizable p opo ion o child en who demons a ed eading and a i hme ic di icul ies in ou sample had in ac dyslexia, dyscal- culia, o bo h. Exis ing esea ch on adolescen eading de elopmen sugges s ha hose who sligh ly lag in hei eading luency de elopmen du ing ea ly g ades o en expe ience a signi ican ly mo e p onounced lag in aca- demic pe o mance immedia ely a e elemen a y school (ages 11–12), as he demands o he cu iculum become inc easingly igo ous and much o seconda y school eaching s a s aking place ou side hei zone o p oximal de elopmen (Blan on e al., 2007; Deshle & Hock, 2007). Simila ly in ma hema ics, high a es o accele a ion in de elopmen ha e been no ed among high pe o me s compa ed wi h low pe o me s, con ibu ing o an inc easing a iance in skills o e ime and a g adually widening skill gap be ween low pe o me s and high pe o me s du ing he ea ly g ades (Aunola e al., 2004); howe e , his p ocess has no been aced o adolescence. Al hough longi udinal esea ch is s ill lacking, exis ing e idence shows ha bo h eading and a i hme ic luency ha e high in e - indi idual s abili y, sugges ing ha e en hough luency de elops o e ime, he indi idual ank o de in skill is es ablished in ea ly yea s and emains ai ly ime-in a ian (Hulslande e al., 2010). Fo his eason, ea ly skills a e s ong p edic o s o la e skills. Fo example, Aunola e al. (2004) epo ed he co ela ion be ween ma hema ical skills (a i hme ic luency asks we e included in he assessmen s) in G ades 1 and 2 o be 0.79, while Eklund e al. (2015) ound ha he co ela ion be ween eading luency sco es in G ades 2 and 8 was 0.78. Despi e such a high s abili y o eading and a i hme ic luency, la ge a iances ha a e unexplained s ill emain, allowing oom o change. This means ha less p edic able de elopmen al pa e ns a e possible, and hey a e usually s udied wi hin RD and MD esea ch. Fo example, RD do no always demons a e longi udinal s abili y (To ppa e al., 2015), e en a e con olling o measu emen e o and using a simula ion-based analysis wi h bu e zones o coun e he e ec s o a bi a y cu -o s (Psy idou e al., 2020). To ppa e al. (2015) ound ha only a ound 40 % o all child en wi h RD in hei sample had pe sis en di icul ies iden i iable in bo h elemen a y and lowe seconda y school (a ages 8 and 14). A simila longi udinal ins abili y was ecen ly obse ed in he iden i ica ion o MD—only abou 50 % o lea ne s wi h an ea ly diagnosis e ained clea di icul ies o e he i s wo yea s o elemen a y school (ages 7 and 8) (Chan & Wong, 2020). These s udies, howe e , ocused on he s abili y o ei he RD o MD wi hou es ing o hei possible como bidi y and i s impac on s abili y. In con as , wo king wi h he same da a se as we used in he p esen s udy Koponen e al. (2018) examined he s abili y o RD and MD as well as como bid di icul ies ac oss G ades 1–4 and ound lowe s abili y in G ade 1 and highe s abili y he ea e . In addi ion, s a ing om G ade 2, como bid di icul ies we e s able and mo e so han he single di icul ies—68 % o second g ade s wi h como bid di icul ies demon- s a ed pe sis en di icul ies in bo h domains and con i med hei s a us in G ade 4, whe eas only 46 % and 39 % o hose wi h single RD and MD, espec i ely, emained in he same de elopmen al g oup. In e es ingly, only 1 %, wen om ypical pe o mance in bo h skills o como bid di icul ies o e ime; howe e , no e ha he s udy ended a G ade 4. The ac ha child en equen ly display como bid di icul ies and may ansi ion om one de ici g oup o ano he o e ime is bes explained by he mul iple de ici model (Penning on, 2006), a heo e - ical amewo k ha accoun s o he eme gence and dynamic na u e o RD and MD by he complex in e ac ions be ween mul iple sha ed isk ac o s ha a e associa ed wi h he wo ypes o di icul ies p obabilis- ically ( a he han de e minis ically). Howe e , u he esea ch ocusing on RD and MD along wi h hei como bidi y and longi udinal s abili y is needed o gain a be e unde s anding o he possible ac o s ha shape di e en de elopmen al pa e ns om a long- e m pe spec i e. 1.2. Family isk o RD and MD The easons behind he di e ences in he pa e ns o eading and a i hme ic luency de elopmen can be mul iple, e.g. child en's cogni- i e skills, mo i a ion- ela ed ac o s, amily ac o s (bo h pa en al eading and ma hema ical skills and he home lea ning en i onmen ), e c. The p esen s udy ocuses on a a ie y o amily ac o s ha migh in luence how child en's skills de elop. In eading, pa en al RD ( amily isk) a e one o he bes ea ly p edic o s o child en's eading skills (Esmaeeli e al., 2019; Puolakanaho, 2007; Van Be gen e al., 2014) while amily isk s udies a e s ill a e in ma hema ics- ela ed esea ch (Shale e al., 2001). Ne e heless win, molecula gene ic, and adop- ion s udies indica e a high he i abili y o di e en ma hema ical skills D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 3 (Bo iello e al., 2020; Doche y e al., 2010; Ko as e al., 2007), including skills such as a i hme ic luency, sugges ing ha pa en al MD could be a s ong p edic o o child en's gene al ma hema ical skills o e ime. Exis ing esea ch on he e iology o como bid di icul ies in eading and ma hema ics- ela ed skills epo ed ha he wo ypes o di icul ies s em la gely om he same gene ic ac o s (Daucou e al., 2020). Mo eo e , eading and a i hme ic luency sha e conside able gene ic o e lap no only wi h one ano he bu also wi h gene al cogni- i e abili y (Ha e al., 2009). Ne e heless, he e a e ew amily isk s udies ha ocus on he como bidi y o RD and MD (Nguyen e al., 2022). Ou p esen s udy o e s no el insigh s in o how di e en pa en al lea ning di icul ies ( amily isk o bo h RD and MD) in luence child en's eading and a i hme ic luency de elopmen . 1.3. Home lea ning en i onmen and pa en al academic assis ance Child en's skills de elop unde he in luence o no only gene ic bu also en i onmen al ac o s which has been unde s ood h ough s udying he home lea ning en i onmen . In esea ch, he home lea ning en i- onmen is commonly di ided in o he home li e acy en i onmen (HLE) and home nume acy en i onmen (HNE) which e e o a -home in- e ac ions be ween pa en s and hei child en, lea ning ma e ials, and pa en al a i udes ela ed o li e acy and nume acy, espec i ely. Mul- iple s udies ha e p oduced compelling e idence indica ing signi ican posi i e associa ions be ween he ea ly home lea ning en i onmen and bo h eading and ma hema ical de elopmen (Dong e al., 2020; Duns e al., 2017). Howe e hese s udies we e conduc ed wi h young chil- d en who we e no ye en olled in o mal schooling (Dong e al., 2020; Duns e al., 2017). S udies wi h child en o school age looking in o pa en al academic assis ance and in ol emen in homewo k a e s ill qui e a e and ha e p o ided mixed e idence. Some s udies wi h gene al popula ion samples o school-age child en sugges ha pa en al aca- demic assis ance is bene icial (Dumon e al., 2012; Pa all e al., 2008), whe eas o he s udies epo a nega i e associa ion be ween pa en al in ol emen and child en's academic pe o mance (Hill & Tyson, 2009; Pome an z & Ea on, 2001). This nega i e associa ion does no neces- sa ily mean ha pa en al in ol emen i sel is de imen al o academic skill de elopmen bu a he ha child en's lowe academic achie e- men likely e okes mo e pa en al academic assis ance (Silinskas e al., 2010; he esea che s used he same da a se as we did bu only he da a om ea ly g ades was a ailable a ha ime). Con adic ing and inconsis en indings could also be a ibu able o he use o di e en esea ch measu es. Fo example, Dumon e al. (2014) highligh ed ha some s udies collec da a on he quan i y o all academic assis ance ac- i i ies whe eas o he s di e en ia e be ween quali a i ely di e en ypes o ac i i ies and show ha only some o hese ac i i ies help child en lea n. Addi ionally, some esea che s ha e poin ed ou ha pa en al lea ning di icul ies could be an impo an con ounding ac o ha needs o be in es iga ed in esea ch on HLE and HNE (Puglisi e al., 2017; Van Be gen e al., 2014). Indeed, pa en s wi h lea ning di icul ies could be o ganizing ewe lea ning ac i i ies a home bu i is no necessa y he eason why hei child en demons a e lowe academic skills, he eal eason could be ha hese child en ha e inhe i ed pa en al lea ning di icul ies. The e o e, he inclusion o bo h home en i onmen al ac o s and pa en al skill measu es is impo an . 1.4. The p esen s udy Ou e iew o p e ious esea ch sugges s ha u he in es iga ion o di e en long- e m pa e ns wi hin skill de elopmen leading o RD and MD a he end o compulso y schooling is impo an . While esea ch ocusing on indi iduals wi h esol ing di icul ies is aluable because i can help iden i y p o ec i e and p omo i e ac o s, i is impo an o ecognize ha esea ch wi h a speci ic ocus on indi iduals wi h below g ade le el ou comes is also aluable because i can help es ablish and be e unde s and speci ic isk ac o s. The he e ogenei y o lea ning di icul ies is mul i-laye ed, as dis inc g oups o di icul ies can be iden i ied based on hei s abili y, ime o eme gence, and co-occu ence wi h o he di icul ies. In iew o his, he p esen s udy aims o add ess wo main esea ch ques ions. The i s is, “Wha pa e ns o de elop- men al p og ess can be iden i ied among hose lea ing comp ehensi e school wi h lowe ounda ional skills ( eading and ma hema ical di icul ies)?” To iden i y he pa e ns o de elopmen al p og ess, we used la en p o ile analysis (LPA), which is cu en ly one o he mos common sci- en i ic app oaches o e ie e homogeneous subg oups (p o iles) om he e ogeneous popula ions. Based on p e ious indings abou he p e alence o como bid RD and MD (Moll e al., 2019), we expec ed o iden i y dis inc g oups o lea ne s wi h RD, MD, and como bid di i- cul ies. Mo eo e , based on p e ious esea ch on de elopmen al changes in he domain o eading (Ca s e al., 2012; To ppa e al., 2015) and ma hema ics (Chan & Wong, 2020), we expec ed o ind pe sis en (eme ging du ing ea ly g ades) and la e-eme ging (eme ging only a e G ade 3) di icul y p o iles. Ou second esea ch ques ion ocused on pa en al in luences: “Do p o iles o low pe o me s di e om one ano he and om ypical pe o me s based on he amily isk s a us (pa en al RD and MD), pa en al educa ion, o home lea ning ac i i ies ( he ea ly home lea ning en i onmen , assessed when child en we e in kinde ga en, as well as pa en al academic assis ance, epea edly measu ed when child en we e in school—in G ades 1–9)?” Taking in o accoun p e ious s udies, we expec ed o ind he ollowing signi ican p edic o s o child en's p o- iles: amily isk as a nega i e p edic o (Esmaeeli e al., 2019; Shale e al., 2001; Van Be gen e al., 2014), he home lea ning en i onmen as a posi i e p edic o (Dong e al., 2020; Duns e al., 2017; Van Be gen e al., 2017), and pa en al academic assis ance as ei he a posi i e (Dumon e al., 2012) o a nega i e p edic o (Hill & Tyson, 2009). To answe he second esea ch ques ion, we compa ed he low pe o me s and ypical pe o me s using one-way ANOVAs. We addi ionally es ed i any o he amily ac o s p edic ed he low pe o ming p o iles using he h ee-s ep app oach in ou LPA (Aspa ouho & Mu h´ en, 2014). 2. Me hods 2.1. Pa icipan s and p ocedu e This s udy is pa o he Fi s S eps S udy (Le kkanen e al., 2006) ha ollowed child en om kinde ga en (aged 6–7 yea s) o G ade 9 (aged 15–16 yea s), he end o comp ehensi e schooling. The sample includes 2614 child en. The s udy ensu ed balanced sampling o pa - icipan s om u al, u ban, and mixed a eas in wes e n, cen al, and eas e n Finland. Ma i al s a uses and educa ional le els o pa icipa ing pa en s we e e y close o he na ional dis ibu ion. O e all, he sample can be conside ed ep esen a i e o he Finnish popula ion in e ms o e hnic composi ion, amily s uc u e and educa ional le els (S a is ics Finland, 2007). The cu en s udy complied wi h he guidelines o he Finnish Na ional Boa d on Resea ch In eg i y (TENK, 2019). The E hical Commi ee o he Uni e si y o Jy ¨ askyl¨ a e iewed he s udy and p o- ided an e hical e alua ion s a emen on June 6 h, 2006. Th oughou he whole s udy esea ch was conduc ed in acco dance wi h he e hical guidelines o esea ch wi h human subjec s. A ound 83 % o all con- ac ed amilies pa icipa ed in he s udy and p o ided in o med consen p io o pa icipa ion. 2.2. Measu es In his s udy, we u ilized da a om eigh a ailable ime poin s (kinde ga en and G ades 1, 2, 3, 4, 6, 7, and 9). Child en's assessmen s we e conduc ed in schools, whe e ained esea che s adminis e ed es s o eading and a i hme ic luency in class ooms. Pa en al ques ion- nai es we e adminis e ed a all ime poin s when child en's skills we e D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 4 assessed, s a ing a kinde ga en. The child en's a he s we e less likely o epo hei home ac i i ies han mo he s (e.g., in G ade 1, 3 % o mo he s' eplies we e missing, whe eas o a he s, his numbe was 33 %). The e o e, only mo he s' sel - epo s we e analyzed (excep o he amily isk ques ionnai e, explained in mo e de ail in he sec ion “Fa- milial isk o RD and MD” below). 2.2.1. Reading luency The measu e o eading luency comp ised h ee s anda d g oup- adminis e ed es s. The i s es was an 80-i em wo d- eading ask ha is pa o he na ionally s anda dized eading es (ALLU; Lindeman, 2000). Each i em o e ed a pic u e along wi h ou phonologically simila w i en wo ds. The ask was o ead he wo ds silen ly and selec he one ha seman ically ma ched he pic u e. Pa icipan s we e allo ed 2 min o comple e his ask, and hei sco e was he sum o all co ec answe s. The pic u es and wo ds used in his es we e simple and amilia o child en. The second eading luency es was a wo d chain ask comp ising 10-wo d chains, each wi h 4–6 wo ds p esen ed in a ow wi hou any spaces (Ne ala & Lyy inen, 2000). Pa icipan s needed o ead he chains silen ly and p o ide bounda y lines be ween all wo ds hey could iden i y. This ask was also ime-limi ed (1.25 min in G ades 1 and 2, 1.20 min in G ade 3, 1.05 min in G ade 4, 1 min in G ades 6 and 7, and 1.30 min in G ade 9), and each pa icipan 's sco e was calcula ed as he sum o all co ec answe s. The hi d eading luency es was a sen ence eading ask. In G ades 1–4, he Finnish e sion o he Tes o Silen Reading E iciency and Comp ehension (TOSREC; Wagne e al., 2010; Finnish e sion by Le kkanen & Poik- keus, 2009) was used. This ask comp ised 60 sen ences, and he du a- ion o comple e he ask was 3 min. Pa icipan s we e asked o ead each sen ence and decide i i was ue o no (e.g., apples a e blue). In G ade 6, a simila ask was adminis e ed— he Finnish adap a ion o he Salzbu g Sen ence Reading Tes (Pichle & Wimme , 2006). Pa icipan s we e asked o e i y he u h ulness o 69 sen ences in 2 min. In G ades 7 and 9, his es was eplaced wi h a simila 3-min assessmen — he s anda dized Finnish eading es o lowe seconda y school sen ence eading (YK¨ A; Le kkanen e al., 2018). This es had he same in- s uc ions, bu he i ems we e designed o olde child en. The inal sum o sco es was also based on he numbe o co ec answe s. The mean o he h ee s anda dized luency measu es was used as he sco e. C on- bach's alpha eliabili y coe icien s o he composi e anged in di e en g ades be ween 0.78 and 0.84. The sco e in each g ade was s anda dized be o e p oceeding wi h analysis. 2.2.2. A i hme ic luency The measu e o a i hme ic luency alloca ed 3 min o comple ion and included one s anda dized g oup-adminis e ed sub es o he a i hme ic es de eloped by Aunola and R¨ as¨ anen (2007). In G ades 1–3, he measu e comp ised 14 addi ion (e.g., 2 +4 =__, 5 +3 +7 =__) and 14 sub ac ion asks (e.g., 8–2 =__, 18–5 −4 =__). In G ade 4, he measu e sligh ly changed and o e ed 25 addi ion and sub ac ion asks (e.g., 117–9 +13 =__; 485–42 =__; 1635 +576 =__) as well as 1 mul iplica ion and 2 di ision asks (e.g., 40:8–3 =__, 240:80 =__, 12 ⋅ 28 =__). In G ade 6, he measu e included 23 addi ion and sub ac ion asks, 3 di ision asks, 1 mul iplica ion ask, and 1 ask wi h decimal numbe s (e.g., 106.2–30.04 =__). Finally, in G ades 7 and 9, he measu e included 19 addi ion and sub ac ion asks, 3 di ision asks, 3 mul i- plica ion asks, and 3 asks wi h decimal numbe s. The sco e on his measu e e lec ed bo h he speed and accu acy o ounda ional ma he- ma ical calcula ions, allowing o assess child en's a i hme ic luency. C onbach's alphas a ied in di e en g ades be ween 0.68 and 0.94. The sco e in each g ade was s anda dized be o e p oceeding wi h analysis. 2.2.3. Familial isk o RD and MD When child en we e in kinde ga en, mo he s and a he s we e asked i hey hemsel es o hei spouse had expe ienced lea ning di icul ies in eading o ma hema ics. Responses we e measu ed on a h ee-poin scale: 1 (no di icul ies), 2 (some di icul ies), and 3 (clea o se ious di i- cul ies). Sel - epo s we e gi en p io i y, whe eas spouse epo s we e used o ill in missingness. The child en we e conside ed o be a amily isk i hey had a leas one pa en wi h some o clea di icul ies. Al hough measu ing pa en al RD and MD wi h a single i em o each di icul y ype does no cap u e all aspec s o amilial isk, p e ious la ge-scale esea ch has shown ha e en a single amilial isk i em can be an impo an p edic o o child en's skills (Esmaeeli e al., 2019). 2.2.4. Pa en al educa ion The pa en s we e asked abou hei educa ion le el as well as ha o he o he pa en using a se en-poin scale: 1 (no oca ional educa ion) (5.1 % o mo he s and 1.8 % o a he s), 2 ( oca ional cou ses) (3.1 % o mo he s and 1.7 % o a he s), 3 ( oca ional school deg ee) (30.8 % o mo he s and 14.3 % o a he s), 4 ( oca ional college deg ee) (23.2 % o mo he s and 10.1 % o a he s), 5 (poly echnic deg ee o bachelo 's deg ee) (9.7 % o mo he s and 4.2 % o a he s), 6 (mas e 's deg ee) (23.7 % o mo he s and 8.0 % o a he s), and 7 (licen ia e o doc o al deg ee) (4.4 % o mo he s and 2.7 % o a he s). The in o ma ion abou pa en al edu- ca ion was collec ed when child en we e in kinde ga en and he sum sco e was compu ed as an a e age o bo h pa en s' indi idual sco es. 2.2.5. Home lea ning en i onmen Fo kinde ga ene s, pa en s comple ed a ques ionnai e abou he lea ning ac i i ies hey o ganized a home. The ques ionnai e was based on i ems de eloped by S´ en´ echal e al. (1998) and S´ en´ echal (2006), which ha e been used success ully in he Finnish con ex (Silinskas e al., 2020). I included ou ques ions abou he equency o home eaching ac i i ies ( eaching le e s, eaching eading, eaching numbe s, and eaching a i hme ic skills). In addi ion, he ques ionnai e had an i em abou sha ed eading: “How o en do you ead books o you child o oge he wi h you child?” All answe s we e gi en on a i e- poin Like - ype scale: 1 (less han once a week), 2 (1–3 imes a week), 3 (4–6 imes a week), 4 (once a day), and 5 (mo e han once a day). The sum sco es o he h ee HLE and wo HNE i ems we e calcula ed by adding he indi idual sco es o ac i i ies ela ed o each domain. C onbach's alphas o HLE and HNE we e 0.79 and 0.86, espec i ely. 2.2.6. Pa en al academic assis ance wi h li e acy asks In each g ade, pa en s we e asked o indica e he equency o di e en li e acy- ela ed ac i i ies o ganized a home using a i e-poin scale anging om 1 (no a all) o 5 (on a daily basis). In G ade 1, he ques ionnai e had wo i ems abou eading (“How o en do you each you child o ead?” and “How o en do you encou age you child o ead independen ly?”). In G ades 2 and 3, he ques ionnai e included ou i ems— wo we e he same as hose in G ade 1 and wo we e abou w i ing (“How o en do you each you child o w i e?” and “How o en do you encou age you child o w i e independen ly?”). In G ade 4, in addi ion o he i ems in he p e ious g ades, wo i ems abou pa en al assis ance we e included (“How o en do you help you child wi h eading homewo k?” and “How o en do you help you child wi h w i ing homewo k?”). In G ades 6, 7, and 9, o ensu e ha he ques- ionnai e is age-app op ia e in ela ion o school subjec s, he i ems abou eading and w i ing we e eplaced wi h equi alen i ems abou Finnish language asks. A hese ime poin s, he ques ionnai e included h ee i ems (“How o en do you each you child o do Finnish language asks?”, “How o en do you help you child wi h Finnish language home assignmen s?”, and “How o en do you encou age you child o do Finnish language asks independen ly?”). Simila i ems ha e been suc- cess ully used in ea lie s udies (e.g., Edwa ds, 2014; Haney & Hill, 2004; Silinskas, Kiu u, e al., 2013). C onbach's alpha coe icien s o he pa en al li e acy assis ance measu e we e 0.55, 0.80, 0.80, 0.89, 0.66, 0.62, and 0.63 in G ades 1, 2, 3, 4, 6, 7, and 9, espec i ely. 2.2.7. Pa en al academic assis ance wi h nume acy asks A simila i e-poin measu e anging om 1 (no a all) o 5 (on a daily D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 5 basis) was used o collec in o ma ion abou he equency o nume acy- ela ed ac i i ies. In G ades 1–3, he ques ionnai e had wo i ems abou ma hema ics (“How o en do you each you child o do calcula ions?” and “How o en do you encou age you child o do calcula ions inde- penden ly?”). In G ade 4, one mo e i em was added ha asked abou pa en al assis ance (“How o en do you help you child wi h calcula ion asks?”). In G ades 6, 7, and 9, he i ems abou calcula ions we e eplaced wi h equi alen i ems abou ma hema ical asks (“How o en do you each you child o do ma hema ical asks?”, “How o en do you help you child wi h ma hema ical home assignmen s?”, and “How o en do you encou age you child o do ma hema ical asks independen ly?”). The majo i y o hese i ems we e based on he li e acy assis ance i ems lis ed abo e (e.g., Edwa ds, 2014; Haney & Hill, 2004; Silinskas, Kiu u, e al., 2013) and ha e been used p e iously by Silinskas e al., 2010. C onbach's alpha coe icien s o he pa en al nume acy assis ance measu e we e 0.67, 0.76, 0.72, 0.81, 0.73, 0.70, and 0.69 in G ades 1, 2, 3, 4, 6, 7, and 9, espec i ely. 2.3. S a is ical analysis A p elimina y s ep was da a p epa a ion: he whole sample was checked o en y e o s and ou lie s. Using Mahalanobis dis ance es , we iden i ied and dele ed 13 mul i a ia e ou lie s. We hen examined he pa e ns o missing da a. Li le's es o missing comple ely a andom (which included all ques ionnai e i ems o li e acy- and nume acy- ela ed ac i i ies o ganized a home) con i med ha mo he s' home ac i i ies epo s we e missing a andom ( χ 2 (5068) =5051.034, p = .564), indica ing ha all mo he s we e equally likely o submi sel - epo s a di e en ime poin s. Ano he Li le's MCAR es was con- duc ed (which included all eading and a i hme ic luency assessmen s om G ades 1 o 9) o de e mine whe he child en's skill pe o mance was associa ed wi h he likeliness o da a missingness. Resul s showed ha child en who pe o med lowe in eading ( χ 2 (165) =314.477, p < .001) and in ma h ( χ 2 (178) =339.301, p <.001) we e mo e likely o no be included in each wa e o he s udy. Mo e de ails on missing alues can be ound in Appendix 1. Nex , o answe he i s esea ch ques ion and o examine he pa - e ns o de elopmen al p og ess ha p eceded s uden s' g adua ion om a comp ehensi e school wi h below g ade le el ounda ional academic skills ( eading and a i hme ic luency di icul ies in g ade 9), we an a ype o mix u e model (LPA; Obe ski, 2016) (Fig. 1). Fo his ype o analysis, we decided no o use he whole sample (N =2151) because o he la ge a iabili y in eading and a i hme ic luency p esen in a gene al popula ion sample. This la ge a iabili y can po en ially p e en LPA om iden i ying dis inc p o iles ha migh exis in he da a (see Huijsmans e al. (2020), who p o ided an example o such p oblem occu ing in LPA). In iew o his, we s a ed ou analysis by sepa a ing low pe o me s om he es o he sample o ensu e ha LPA could e ie e dis inc p o iles om he popula ion o in e es — ha is, he pa icipan s wi h lea ning di icul ies a he end o comp ehensi e school. Composi e sco es o eading luency in G ade 9 and a i hme ic luency in G ade 9 we e calcula ed and e e yone who pe o med a leas one s anda d de ia ion below he mean ( he mean was calcula ed based on he whole sample) in ei he eading luency o a i hme ic luency we e conside ed o be a low-pe o ming adolescen . In o al, he sco es o 391 adolescen s we e below he cu -o o eading luency, a i hme ic luency, o bo h. Table 1 p esen s he desc ip i e s a is ics o his g oup. Once he popula ion o in e es was selec ed ( hose g adua ing om school wi h low ounda ional academic skills), LPA was conduc ed o hese 391 pa icipan s. Based on hei pe o mance on all eading and a i hme ic luency asks (using con inuous s anda dized a iables) ac oss all se en ime poin s (G ades 1–9), we examined whe he dis inc p o iles exis ed (Mu hen, 2001) using Mplus e sion 7.3. Se en in- dica o s o eading luency and se en indica o s o a i hme ic luency (one o each ime poin ) we e en e ed in o ou mix u e model as in- dica o s. The numbe o indica o s we e deemed app op ia e o his esea ch ques ions based on he indings o Wu p s and Geise (2014), which es ablished ha adding mo e indica o s in mix u e models im- p o es hei pe o mance and can compensa e o small sample sizes. Ou mix u e model pe o med well wi hou unning in o any p oblems Fig. 1. La en p o ile analysis model o he eading and a i hme ic luency measu es. No e. C ep esen s he la en p o iles, Le el RF and Le el AF ep esen he ini ial le el o eading luency (RF) and a i hme ic luency (AF). Numbe s nex o RF and AF indica e he assessmen ime poin (g ade). D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 6 Table 1 Desc ip i e s a is ics o all a iables ac oss ime. Whole sample Low pe o me s only N Minimum Maximum Mean SD Skewness (s d. e o ) Ku osis (s d. e o ) N Minimum Maximum Mean SD Skewness (s d. e o ) Ku osis (s d. e o ) Reading luency (z-sco es) G ade 1 2037 −2.44 4.02 0.00 1.00 0.62 (0.05) 0.44 (0.11) 276 −1.98 2.03 −0.54 0.68 0.55 (0.15) 0.14 (0.29) G ade 2 1991 −2.89 3.89 0.00 1.00 0.26 (0.05) 0.23 (0.11) 280 −2.16 2.69 −0.58 0.74 0.47 (0.15) 1.39 (0.29) G ade 3 1980 −4.42 3.19 0.00 1.00 −0.04 (0.05) 0.43 (0.11) 287 −2.72 2.46 −0.59 0.83 0.47 (0.14) 0.66 (0.29) G ade 4 1939 −4.62 2.76 0.00 1.00 −0.17 (0.05) −0.30 (0.11) 286 −2.64 2.16 −0.62 0.84 0.34 (0.14) 0.16 (0.29) G ade 6 1807 −3.58 3.28 0.00 1.00 0.10 (0.05) −0.11 (0.11) 365 −2.92 2.61 −0.75 0.90 0.58 (0.13) 0.76 (0.25) G ade 7 1755 −4.20 3.04 0.00 1.00 −0.07 (0.05) −0.00 (0.12) 369 −4.13 2.11 −0.87 0.90 0.25 (0.13) 0.47 (0.25) G ade 9 1706 −2.98 2.99 0.00 1.00 −0.09 (0.05) −0.14 (0.12) 391 −2.98 2.88 −1.02 0.93 0.82 (0.12) 1.12 (0.25) A i hme ic luency (z-sco es) G ade 1 2035 −2.55 4.25 0.00 1.00 0.33 (0.05) 0.26 (0.11) 275 −2.55 2.07 −0.44 0.78 0.25 (0.15) −0.16 (0.29) G ade 2 1986 −3.28 2.44 0.00 1.00 −0.09 (0.05) −0.46 (0.11) 278 −2.47 1.83 −0.53 0.86 0.27 (0.15) −0.32 (0.29) G ade 3 1979 −4.25 1.82 0.00 1.00 −0.64 (0.05) 0.45 (0.11) 287 −3.39 1.60 −0.56 0.96 −0.07 (0.14) −0.25 (0.29) G ade 4 1938 −4.18 2.44 0.00 1.00 −0.63 (0.06) 0.80 (0.11) 286 −3.20 1.71 −0.65 0.89 −0.33 (0.14) 0.35 (0.29) G ade 6 1802 −4.14 2.63 0.00 1.00 −0.27 (0.06) 0.17 (0.11) 365 −4.14 2.09 −0.80 0.88 −0.21 (0.13) 0.53 (0.25) G ade 7 1734 −3.61 3.50 0.00 1.00 −0.16 (0.06) 0.35 (0.12) 367 −3.61 1.39 −0.81 0.86 −0.06 (0.13) 0.22 (0.25) G ade 9 1690 −3.56 3.09 0.00 1.00 −0.11 (0.06) 0.02 (0.12) 391 −3.56 1.56 −1.03 0.88 0.41 (0.12) 0.43 (0.25) Pa en al academic assis ance wi h li e acy asks (mean composi es o i ems) G ade 1 1474 1 5 2.94 0.91 0.19 (0.06) −0.39 (0.13) 203 1 5 3.24 0.91 0.28 (0.17) −0.29 (0.34) G ade 2 1430 1 5 2.29 1.05 0.69 (0.06) 0.24 (0.13) 200 1 5 2.60 0.83 0.44 (0.17) −0.15 (0.34) G ade 3 1360 1 5 2.06 0.95 0.79 (0.07) 0.76 (0.13) 198 1 4.50 2.31 0.72 0.64 (0.17) 0.52 (0.34) G ade 4 1269 1 5 1.85 0.97 0.92 (0.07) 1.19 (0.14) 187 1 4.50 2.05 0.67 0.55 (0.18) 0.59 (0.35) G ade 6 999 1 4 1.95 0.59 0.29 (0.08) −0.08 (0.15) 182 1 4 2.19 0.53 0.22 (0.18) 0.73 (0.36) G ade 7 768 1 3.67 1.83 0.57 0.30 (0.08) −0.33 (0.18) 141 1 3.67 2.03 0.57 0.11 (0.20) −0.08 (0.41) G ade 9 892 1 4 1.73 0.54 0.45 (0.08) 0.02 (0.16) 169 1 3.33 1.87 0.53 0.10 (0.19) −0.44 (0.37) Pa en al academic assis ance wi h nume acy asks (mean composi es o i ems) G ade 1 1470 1 5 2.93 0.89 0.13 (0.06) −0.47 (0.13) 202 1 5 3.18 0.93 0.10 (0.17) −0.53 (0.34) G ade 2 1440 1 5 2.45 0.91 0.44 (0.06) −0.23 (0.13) 203 1 5 2.77 0.96 0.23 (0.17) −0.53 (0.34) G ade 3 1362 1 5 2.31 0.82 0.49 (0.07) 0.22 (0.13) 197 1 4.50 2.55 0.77 0.18 (0.17) −0.60 (0.34) G ade 4 1280 1 5 2.16 0.76 0.68 (0.07) 0.50 (0.14) 188 1 5 2.42 0.78 0.54 (0.18) 0.45 (0.35) G ade 6 987 1 4.67 2.07 0.66 0.39 (0.08) 0.20 (0.16) 180 1 4 2.33 0.66 0.41 (0.18) 0.26 (0.36) G ade 7 765 1 5 1.90 0.65 0.57 (0.09) 0.50 (0.18) 140 1 3.57 2.09 0.66 0.10 (0.20) −0.59 (0.41) G ade 9 890 1 4 1.71 0.61 0.73 (0.08) 0.45 (0.16) 169 1 4 1.93 0.60 0.37 (0.19) 0.12 (0.37) D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 7 leading us o conclude ha we had an adequa e balance be ween he sample size and model indica o s. Maximum likelihood wi h obus s anda d e o s was used o es ima e model pa ame e s. Mo eo e , missing da a was handled using ull in o ma ion maximum likelihood es ima ion (FIML). Mix u e models do no ha e one commonly accep ed c i e ion o deciding he numbe o classes (p o iles); he e o e, we elied on se e al s a is ical in o ma ion c i e ia as well as on he in e - p e abili y o he inal solu ion and g aphic p esen a ions o all possible solu ions o decide he numbe o classes (p o iles indica ed by he model) (Yu & Pa k, 2014). No e ha heo y and pas indings play an impo an ole in he decision (Be lin e al., 2014; Geise , 2012). Nex , we alida ed he classi ica ion by conduc ing epea ed mea- su es analysis o a iance (ANOVA) on child en's skills. To de e mine whe he child en's RD and MD we e associa ed wi h amily- ela ed a iables, we conduc ed chi-squa e es s and ANOVAs. This second pa o he analysis was conduc ed in SPSS S a is ics 26. Finally, using he “ h ee-s ep app oach” we added all amily- ela ed ac o s as p edic o s o ou mix u e model (Aspa ouho & Mu h´ en, 2014). This s a is ical app oach allows co a ia es o be es ed as p e- dic o s o la en p o iles in a mul inomial logis ic eg ession by using he Bolck-C oon-Hage naa s (BCH) me hod (Aspa ouho & Mu h´ en, 2014; Bakk e al., 2016). The BCH me hod uses weigh s based on he pos e io p obabili ies o adjus o classi ica ion e o . To analyze he ela i e con ibu ion o each p edic o o he iden i ied la en p o iles, we con- duc ed hie a chical eg ession analyses in a s uc u al equa ion modeling (SEM) amewo k by applying a Cholesky model (De Jong, 1999). Two sepa a e Cholesky models we e used, one model examined he ela i e con ibu ion o he ac o s ela ed o li e acy (pa en al eading di icul ies, eaching li e acy a home when child en we e in kinde ga en, pa en al assis ance wi h li e acy asks in G ades 1–9, pa en al educa ion) and he o he model examined he ela i e con i- bu ion o he ac o s ela ed o nume acy (pa en al ma h di icul ies, eaching nume acy a home when child en we e in kinde ga en, pa en al assis ance wi h nume acy asks in G ades 1–9, pa en al edu- ca ion). Pa en al educa ion was ea ed as a gene al con ol measu e and hus en e ed in bo h models. Maximum likelihood es ima ion wi h obus s anda d e o s (MLR) was used as es ima o o he analysis. The second hal o ou analysis ha included amily- ela ed ac o s (using chi-squa e es s, ANOVAs, and he h ee-s ep app oach) was pe o med o answe he second esea ch ques ion. All hese analy ical p ocedu es we e pe o med wi h he same goal in mind, bu hey had impo an di e ences. Compa ed o ANOVAs and chi-squa e es s he h ee-s ep app oach is a mo e eliable me hod o iden i y ac o s ha a e signi ican ly associa ed wi h la en p o iles, howe e in he p esen s udy he h ee-s ep app oach could no include ypical pe o me s o compa ison ( his was only possible in ANOVAs). Thus, only he combina ion o di e en s a is ical app oaches allowed us o answe he second esea ch ques ion comp ehensi ely. 3. Resul s 3.1. Desc ip i e s a is ics and g oup compa isons Table 1 p esen s he desc ip i e s a is ics o child en's skills and pa en al academic assis ance measu es o all pa icipan s. All o he measu e dis ibu ions we e close o no mal dis ibu ion. 3.2. Iden i ica ion o pa e ns wi hin de elopmen leading o RD and MD in G ade 9 To examine he p esence o di e en ial pa e ns wi hin skill de el- opmen ha lead o RD, MD, o bo h in G ade 9, we an a se ies o LPA models. Fig. 1 depic s he LPA model, and Table 2 desc ibes he LPA model ou comes o he i s six p o iling solu ions. Models beyond six p o iles became uns able and i ed he da a poo ly. Six- and i e-p o ile models each had one e y small p o ile (con aining only se en people, which is <2 % o he sample). In he ou -p o ile model, he a e age la en class p obabili ies declined below 0.80, sugges ing g ea e un- ce ain y o his p o ile solu ion. In addi ion, BIC s a ed inc easing in he ou -p o ile model, indica ing a wo sening i , which con inued h ough o he i e and six p o ile models. The wo-p o ile model had he highes en opy, and LMR and VLMR p- alues sugges ed ha wo p o- iles a e su icien . Howe e , he h ee-p o ile model had he lowes BIC alue. We chose he h ee-p o ile model ins ead o he wo-p o ile o wo easons. Fi s , BIC has been epo ed o be he mos e icien indi- ca o o deciding he numbe o la en classes (p o iles) (Yu & Pa k, 2014), especially when dealing wi h con inuous a iables (Fonseca & Ca doso, 2007). Second, he h ee-p o ile model was be e i ed o heo y, which is a s ong a gumen in i s a o (Geise , 2012), because i included a dis inc como bid g oup whe eas he wo-p o ile model did no . The i s p o ile (N =121) was named Reading Di icul ies (RD), as he pa icipan s in his p o ile demons a ed low eading luency bu a e age a i hme ic luency. The second p o ile (N =176) was named Reading and Ma hema ical Di icul ies (RD&MD), as i was cha ac e - ized by low eading and a i hme ic luency. Finally, he hi d p o ile (N =94) was named Ma hema ical Di icul ies (MD) in iew o he pa - icipan s ha ing low a i hme ic luency bu a e age eading luency. Fig. 2 shows he eading and a i hme ic luency de elopmen in he low-pe o ming p o iles con as ed wi h ypical pe o me s. As can be seen in bo h Fig. 2 and Table 3, child en wi h only RD signi ican ly unde pe o med no only in eading luency asks bu also in a i hme ic Table 2 Fi indices o la en p o ile analyses (low pe o me s only, N =391). Numbe o p o iles BIC aBIC AIC En opy p-Value o LMR p-Value o VLMR n in class 1 (ALCP) n in class 2 (ALCP) n in class 3 (ALCP) n class 4 (ALCP) n class 5 (ALCP) n class 6 (ALCP) 1 10,448.398 10,311.961 10,277.744 2 10,304.732 10,120.701 10,074.547 0.83 0.0010 0.0010 287 (0.964) 104 (0.925) 3 10,278.694 10,047.068 9988.978 0.73 0.3347 0.3303 176 (0.853) 121 (0.893) 94 (0.902) 4 10,293.652 10,014.433 9944.406 0.72 0.1931 0.1902 79 (0.809) 109 (0.776) 82 (0.908) 121 (0.875) 5 10,316.166 9989.352 9907.390 0.76 0.8263 0.8258 57 (0.89) 204 (0.84) 70 (0.80) 53 (0.84) 7 (0.96) 6 10,340.258 9965.85 9871.951 0.77 0.2548 0.2542 160 (0.81) 24 (0.88) 64 (0.82) 78 (0.88) 58 (0.83) 7 (0.97) No e. BIC =Bayesian In o ma ion C i e ion; aBIC =Adjus ed Bayesian In o ma ion C i e ion; AIC =Akaike's In o ma ion C i e ion; LMR =Lo-Mendell-Rubin Adjus ed Likelihood Ra io Tes ; VLMR =Vuong-Lo-Mendell-Rubin Likelihood Ra io Tes ; ALCP =A e age La en Class P obabili ies o Mos Likely La en Class Membe ship by La en Class. D. Khanolainen e al. Lea ning and Indi idual Di e ences 105 (2023) 102321 8 luency asks compa ed wi h ypical pe o me s o e all ime poin s. Howe e , RD g adually made mo e gains in a i hme ic luency han MD and RD&MD and p og essed owa ds he skill le el o ypical pe o me s by g ade 9. Simila ly, Fig. 2 sugges s ha child en in ea ly g ades wi h only MD pe o med wo se han ypical pe o me s in eading luency asks; howe e , he di e ence be ween hese g oups was no s a is ically signi ican (Table 3). Mo eo e , RD and MD g adually di e ged in hei skill gains (child en wi h RD caugh up wi h ypical pe o me s in a i hme ic luency, whe eas child en wi h MD only na owed he gap wi h ypical pe o me s in eading luency). RD&MD lagged inc easingly on bo h skills o e all ime poin s. In iew o he use o s anda dized eading and a i hme ic sco es, he downwa d pa e ns seen in Fig. 2 indica e a g owing gap in g ade le el pe o mance ac oss he p o iles, bu hey do no imply ac ual skill de e io a ion. 3.3. P o ile di e ences in pa en al cha ac e is ics Fi s , chi-squa e es s we e pe o med o examine he ela ionship be ween pa en al di icul ies ( amily isk) and p o ile membe ship, including ypical pe o me s (Table 4). Family isk o RD was no Fig. 2. Reading luency (z-sco es) and a i hme ic luency (z-sco es) longi udinal pa hways o di e en p o iles ac oss he se en ime poin s. No e. RD =Reading Di icul y P o ile; MD =Ma hema ical Di icul y P o ile; RD&MD =Como bidi y P o ile; TP = ypical pe o me s (added he e o compa ison bu was no iden i ied in LPA). E en hough child en's skills ac oss all p o iles we e con inuously de eloping o e ime, he g aph shows some downwa d pa e ns. This is because s anda dized sco es o age-app op ia e measu es we e used o plo ing his line g aph, ep esen ing he ela i e pe o mance compa ed o g ade le el pee s. Table 3 Desc ip i e s a is ics and ANOVA compa isons o skill measu es (z-sco es) o di e en p o iles. Measu es Time poin Typical pe o me s (TP) RD RD&MD MD F Pa ial e a sq Signi ican pai wise di e ences be ween p o iles (Bon e oni compa isons) N M (SD) N M (SD) N M (SD) N M (SD) Reading luency G 1 1761 0.08 (1.01) 99 −0.69 (0.65) 109 −0.61 (0.60) 68 −0.23 (0.76) 36.43*** 0.05 RD, RD&MD <TP; RD <MD G 2 1711 0.09 (1.00) 100 −0.79 (0.68) 111 −0.69 (0.64) 69 −0.09 (0.75) 46.76*** 0.07 RD, RD&MD <TP, MD G 3 1693 0.10 (0.99) 103 −0.90 (0.67) 112 −0.72 (0.73) 72 −0.06 (0.84) 57.68*** 0.08 RD, RD&MD <TP, MD G 4 1653 0.10 (0.99) 103 −0.93 (0.71) 113 −0.83 (0.67) 70 0.18 (0.74) 69.33*** 0.10 RD, RD&MD <TP, MD G 6 1442 0.19 (0.93) 116 −1.13 (0.61) 158 −1.06 (0.68) 91 0.27 (0.76) 162.90*** 0.21 RD, RD&MD <TP, MD G 7 1386 0.23 (0.89) 117 −1.30 (0.67) 160 −1.12 (0.73) 92 0.12 (0.67) 214.86*** 0.27 RD, RD&MD <TP, MD G 9 1315 0.30 (0.80) 121 −1.55 (0.43) 176 −1.34 (0.59) 94 0.27 (0.68) 427.01*** 0.43 RD, RD&MD <TP, MD A i hme ic luency G 1 1760 0.07 (1.01) 99 −0.33 (0.89) 108 −0.47 (0.74) 68 −0.55 (0.67) 21.87*** 0.03 RD, MD, RD&MD <TP G 2 1708 0.09 (0.99) 100 −0.31 (0.90) 109 −0.60 (0.89) 69 −0.74 (0.68) 34.60*** 0.05 RD, MD, RD&MD <TP; MD <RD G 3 1692 0.09 (0.97) 103 −0.19 (1.00) 112 −0.80 (0.93) 72 −0.74 (0.79) 46.32*** 0.07 RD, MD, RD&MD <TP; RD&MD, MD <RD G 4 1652 0.11 (0.97) 103 −0.23 (0.85) 113 −0.91 (0.87) 70 −0.84 (0.72) 61.76*** 0.09 RD, MD, RD&MD <TP; RD&MD, MD <RD G 6 1437 0.20 (0.92) 115 −0.18 (0.72) 159 −1.12 (0.87) 91 −1.01 (0.64) 147.67*** 0.20 RD, MD, RD&MD <TP; RD&MD, MD <RD G 7 1367 0.22 (0.92) 115 −0.07 (0.65) 160 −1.18 (0.73) 92 −1.08 (0.71) 170.45*** 0.23 RD, MD, RD&MD <TP; RD&MD, MD <RD G 9 1299 0.31 (0.81) 121 −0.05 (0.63) 176 −1.40 (0.63) 94 −1.59 (0.38) 405.09*** 0.42 RD, MD, RD&MD <TP; RD&MD, MD <RD No e. * p<.05, ** p<.01, *** p<.001. D. Khanolainen e al.